How ILX Calcs is tested

The method

1. Golden tests against published examples

   Worked examples and tables from publications such as the AISC Design Examples and Design Guides, the NDS and AWC guides, ASCE 7-22, TMS, AISI and SSMA, FEMA and other government manuals are entered as test cases. ILX Calcs runs each one, and every value is compared with the published value, within a stated tolerance.

2. Hand calculations where nothing is published

   Where no worked example runs through the whole calculation, the test cases are hand calculations in closed form, from the equations of the code, each value worked out independently of the program.

3. Documented differences

   When a published value and ILX Calcs differ (a rounding choice, a simplification in the example, an error in the published value or a newer provision), the reason is written down and listed with the results. Nothing is quietly skipped.

4. Thousands of automated tests

   Beyond the worked examples, an automated test suite checks unusual inputs, US and metric units, LRFD and ASD, reports, drawings and edge cases. It runs on every change before a release.

Live results

Straight from the verification results that ship with this release.

Release 1.0.0, results generated 2026-11-13. 9,654 individual values compared in 3,141 runs (LRFD and ASD where the code offers both); 9,654 of them match or have a documented reason.

51 of the calculation types have only hand calculations so far, no published example: AAC masonry wall, Atmospheric ice loads, Beam grid (grillage), Bond beam chord and collector, Built-up cold-formed steel member, Cold-formed steel bypass and infill framing, Cold-formed steel ceiling framing, Cold-formed steel clip angle, Cold-formed steel floor vibration, Cold-formed steel girt, Cold-formed steel jamb studs, Cold-formed steel parapet, Cold-formed steel shear wall chord studs, Cold-formed steel sloped and mansard wall, Cold-formed steel soffit framing, Cold-formed steel special bolted moment frame, Cold-formed steel storage rack, Cold-formed steel track, Cold-formed steel truss bracing, Concrete stair, Corbelled masonry, Curved and tapered glulam, Dapped-end beam, Fall-protection anchorage, Fluid and hydrostatic pressure, Freestanding masonry wall, Gabion retaining wall, Gravity retaining wall, Helical pile, Joist and waffle slab, Laterally loaded pile (p-y), Ledge and inverted-tee beam, Liquefaction triggering, Liquid-containing tank wall, Masonry arch, Masonry bearing, Masonry chimney, Masonry parapet, Micropile, Modal response spectrum, Movement joints, Notched and tapered member ends, Pile capacity from CPT, Prestressed concrete beam, Roof geometry, Roof ponding, Segmental retaining wall, Seismic member checks, Special moment frame members, Wood shrinkage and moisture, Wood stair.

Documented differences

• Worked stiffness uses the three span factor on four spans. The Vulcraft 2016 catalog works the stiffness of a four span panel on page 11 and prints about 98 kips per inch. Its calculation multiplies the warping term by 0.90, which its own table, and AISI S310 Table 1.3-1, give for three spans. Four spans take 0.80. The warping and slip terms of the example match. ILX Calcs gives 101 kips per inch, 3 percent stiffer than the printed value, as the code's table asks. With 0.90 the two agree.
• Weld tension in a catalog table below the code equation. Table 2 of the Vulcraft 2016 catalog gives 588 pounds allowable for a 3/4 inch arc spot weld on 22 gage, or 1,470 pounds nominal. AISI S100 Equation J2.2.3-2 at the 62 and 50 ksi steel the catalog states gives 1,621 pounds. The ratio is the same at every gage, so the catalog has used a different steel ratio or factor it does not state. ILX Calcs follows the code equation, 10 percent above the catalog's tension value. That is the less conservative side. It enters only the interaction of shear and wind uplift at a weld. The strength in shear of the same welds matches the catalog.
• Catalog wind tables with uplift use an older interaction. The Vulcraft 2016 catalog's wind tables with net uplift use an older interaction and a diaphragm safety factor of 2.35, where AISI S310-20 has 2.00. Applied to the catalog's own fastener strengths at 60 psf, the S310 equations give a nominal shear of 1,462 plf against the 1,483 plf the table implies. ILX Calcs is 1.4 percent below, the conservative side. The tables without uplift match within 1 percent. The S310 uplift equations have no published worked example here.
• Cantilever moment read off a chart. UFS 3-220-20 Figure 4-43 reads a moment ratio of 0.6 off its chart, to one digit, and gets 31,590 lb-ft per foot using 62.4 pcf, though the example states a soil of 122.4 pcf with 60 pcf buoyant. Equilibrium of the net pressure on the stated soil gives 29,190 lb-ft per foot. The depth matches within 5 percent. ILX Calcs is 8 percent below the printed moment. That is the less conservative side. The second chart example, with clay, matches within 5 percent. No line-by-line published cantilever has been run: use judgment.
• One influence factor read off a chart by eye. UFS 3-220-20 Figure 4-17 has no printed table, so its influence factors were read by eye, and a reading is good to about 0.005. At m = 2.0 the reading is 0.22 and the integrated stress gives 0.2251, just past the comparison's limit of 0.005. ILX Calcs is 0.005 above the reading, the conservative side for pressure on a wall. The other four readings on this chart are within the limit.
• Negative moments said to be at the support face. ACI SP-17 (2014) One-way Example 3 states 12 in. supports and moments at the faces, and prints 6.4 and 5.2 kip-ft with the hyperstatic moment at the second and middle supports. At the face this type gives 5.4 and 4.4 kip-ft. At the support centerline it agrees with the source within 5 percent, which suggests the printed values may be centerline values, but the source does not say so. ACI MNL-17(21) One-way Slab Example 3 (p. 78) prints the same moments with the same label: gravity 7.2 and 5.7, hyperstatic 0.8 and 0.5, design 6.4 and 5.2 kip-ft. Its own moment diagrams (Figs. E3.5 and E3.7) put these peaks on the support centerlines, and its cantilever moment of 0.8 kip-ft is the centerline value (0.166 kip/ft times 3 ft squared over 2 is 0.75), where the face would give about 0.5. The printed values are centerline moments under a face label. ILX Calcs matches the printed moments at the centerline, its default, and the 2021 example is tested there. At the face it gives 5.4 and 4.4 kip-ft by statics, as 7.4.2.1 permits; that is a lower demand only because the section is the face, not an unsafe reading.
• Line load resultant at a distance of 0.4 of the wall height. UFS 3-220-20 Figure 4-19 prints a resultant of 0.55 times the load for distances up to 0.4 of the wall height. The printed equation for those distances integrates over the wall height to 0.539. The figure's other equation, for greater distances, gives 0.552 at 0.4. ILX Calcs integrates the printed pressure, 2 percent below the printed resultant. The pressure at each depth matches the figure, and its resultant follows from that.
• Hyperstatic moment at the second support. ACI SP-17 (2014) prints 0.8 kip-ft from a commercial program, rounded to 0.1. Load balancing on the printed force, eccentricities and spans gives 0.74 kip-ft. ILX Calcs gives 0.74 kip-ft. This lowers the negative moment at the support by 0.06 kip-ft less than the source, about 1 percent, and raises the span moment by less.
• Joint strength coefficient under the 2019 code. ACI SP-17 (2014) follows ACI 318-14 and prints a joint strength of 611 kips, from the coefficient 15. ACI 318-19 Table 15.4.2.3 gives 20 for a joint with column and beam continuing past it and not confined by transverse beams. ACI MNL-17(21) Columns Examples 2 and 3 (pp. 410 and 417), to ACI 318-19, take 20 for this joint and print 814 kips, which ILX Calcs matches (tested). ILX Calcs gives 815 kips, following ACI 318-19. A published example to ACI 318-19 has not been run.
• Column shear from the printed moments. ACI SP-17 (2014) prints a column shear of 52 kips. Its printed moments of 6,520 and 2,960 kip-in., beam shears of 77 and 30 kips, column depth of 24 in. and height of 192 in. give 56 kips by the printed formula. ACI MNL-17(21) Columns Example 3 (p. 416) repeats the inputs and the 52 kips. Its Example 2 (p. 409) applies the same formula correctly, (6,520 + 1,970 + (70 + 35) times 12) / 192 = 51 kips, which ILX Calcs matches (tested). ILX Calcs gives 56 kips from those moments, which lowers the joint shear by 4 kips, about 1 percent. With the column shear entered, it gives the printed result.
• Downward pressure on roof zone 1 prime. For the school, the NCSEA table prints 12.5 psf downward on roof zone 1 prime, the same as the other roof zones. That uses a directionality factor of 0.75. Its own uplift value for the zone uses 0.90, which is what ASCE 7-22 Table 32.6-1 gives for zone 1 prime without a limit to uplift. ILX Calcs gives 13.3 psf, on the safe side by 0.8 psf. It applies to this one downward value. Uplift matches the source.
• A misprint in the WoodWorks table of chord deformation without take-up devices. The table prints 0.466 in. at the 4th level. Its own columns on that row add to 0.418 in., which with the wall length over the lever arm gives 0.446 in., and the accumulated column of the same table follows 0.446 in. ILX Calcs gives 0.446 in. at that level, and matches the accumulated values the table prints.
• Height used in the FEMA table of CLT shear wall deflection. The FEMA equation defines the height as the panel height. The shear and total columns of its table, at the two stories under a floor, come out only with the floor panel above added to that height. ILX Calcs uses the panel height, as the equation is written. The shear term and the total deflection at those two stories are about 0.01 in. lower than printed: 0.319 in. against 0.33 in., and 0.338 in. against 0.35 in. Both remain well under the allowable 0.95 in. in the example. This is on the lower side of the printed value, and it is stated in the chapter.
• One rounded cell of the lap splice table. The Masonry Designers' Guide table of lap lengths rounds up to whole inches, for example 19.47 in. to 20 in. For a No. 3 bar at 2 in. cover and a masonry strength of 2,000 psi the equation gives 12.27 in., and the table prints 12 in., where rounding up gives 13 in. ILX Calcs gives 12.27 in. and rounds it up to 13 in. in this comparison, half an inch longer than the table. The other 71 values of the table agree.
• Percent drift printed in the APA force transfer worksheet. The worksheets in APA Technical Note T555C print a drift of 0.0147 and 0.0137 percent for deflections of 0.352 and 0.329 in. on an 8 ft wall. Both are the deflection divided by 24. The deflection over the 96 in. height is about 0.37 percent. ILX Calcs does not print a percent drift for this wall. The deflection agrees with the note; only the printed percentage differs.
• The four-term deflection equation. APA Technical Note T555C shows the deflection two ways: 0.329 in. by the four-term equation of the 2021 IBC and 0.352 in. by the three-term equation of SDPWS 2021. ILX Calcs has the three-term equation of the code it follows, which the note says gives the larger deflection here. ILX Calcs gives 0.352 in., 7 percent above the four-term result, matching the note's own three-term figure.
• Shape dimensions of 1986 in a web opening example. AISC Design Guide 2 Example 3 uses the 1986 shape tables: a W21X44 is 20.66 in. deep and its top tee 4.83 in. The current shape table prints 20.7 in., so the tee is 4.85 in. The secondary moment ratio of the tee comes out 1.60 here and 1.62 in the guide. About 1.2 % on that ratio. The shear strength that follows from it agrees within 1 %.
• Stud capacity changes within a web opening example. AISC Design Guide 2 Example 4 computes 26.0 kips per stud on one page and uses 26.1 kips on the next, then rounds the concrete force at the low moment end to 127 kips. The distance to that force comes out 0.414 in. here and prints as 0.42 in. No effect on any strength beyond the rounding: the top tee's shear agrees within 1 %.
• Assumed bar position in a web opening example. AISC Design Guide 2 Example 4 assumes the bar centroid 3.995 in. from the flange when it works out the bottom tee, then adopts a bar that puts it at 3.93 in., and notes that the value is somewhat less than assumed. This program uses the bar as it is. The ratio is 1.46 against 1.48. The guide says the section remains adequate; the bottom tee's shear agrees within 1 %.
• Two values of the same ratio in a web opening example. AISC Design Guide 2 Example 4 computes the secondary moment ratio of the reinforced top tee as 8.35 on p. 34 and uses 9.05 on p. 35. Its own numbers give 8.35, which is what this program finds, for a shear ratio of 1.43 where the guide prints 1.55. None on the result: the pure shear limit of the top tee, Eq. 3-21, governs with either value, and the shear strengths match.
• Tee compression strength printed in AISC Design Guide 31. Examples 4.1 and 4.2 of the guide say the warping term is left out of the tee's torsional buckling stress, yet the printed stress still contains it, as if the warping constant were 1 in. to the sixth. Their top tees also measure the distance to the shear center from the tip of the stem, where it belongs at the flange: Example 4.3 does it correctly on its bottom tee. This program applies Section E4 of the specification with the true shear center, with the warping term left out as the User Note allows, or with the tee's own warping constant if selected. It has no option to use the printed values. The available compression of the tee is 51.6 kips here against the 64.9 kips printed for Example 4.1, and 51.7 kips against 65.6 kips for Example 4.2, so the printed strengths are about 26 % high, on the unsafe side. Under LRFD the largest ratios rise from 0.741 to 0.936 and from 0.759 to 0.975, and both beams pass. Under ASD they rise from 0.815 to 1.03 and from 0.835 to 1.07: both beams the guide shows as adequate fail on tee compression here. With the tee's own warping constant, the other option, the ASD ratios are 0.904 and 1.00. Examples 4.3 and 4.4 are not affected, because their tees carry no compression.
• Flexural constant printed in Example 4.1. Example 4.1 divides by the square of the polar radius of gyration squared a second time and prints a flexural constant of 0.880. On the guide's own numbers it would be about 0.25, and with the true shear center about 0.83, which this program uses. No effect of its own on the result here, because the torsional stress is far below the flexural one. It is part of the difference recorded for the tee compression strength.
• Web post strength of a cellular beam, sensitive to rounding. The strength ratio of a cellular web post is a small difference between large terms. The guide prints 0.450 in Example 4.2 and 0.466 in Example 4.4 after rounding the coefficients. This program carries them unrounded and gets about 0.42 and 0.44. The web post strength here is about 6 % lower than printed, on the safe side. Both examples still pass.
• Horizontal shear printed in Example 4.4, ASD. The example's own expression, 84.0 kips divided by 1.50, gives 56.0 kips. It prints 50.3 kips. This program gives 56.0 kips, 11 % above the printed number and the same as Example 4.3, which has the same post. The ratio stays well below 1.
• Moments of inertia in Example 4.4. At the net section, the example takes the top tee's centroid distance measured from the stem tip as if it were measured from the flange, in its effective depth, its neutral axis and its moment of inertia, and prints 1,710 in. to the fourth. Example 4.3 does the same step correctly, and that way this example gives 2,078. Its composite value then takes the area ratio of the critical section and prints 5,100; this program gets 5,518 from the net section's own values. The moments of inertia here are about 22 % and 8 % higher than printed, and the deflections lower: 1.14 in. against 1.39 in. on the steel alone, on the unsafe side of the printed numbers but from the correct section. Strength is not affected, because the example takes the tee forces from the critical section. The example passes its limits either way.
• Rounded section values in Example 4.2. The example carries its depths at three figures, which moves the tee's moment of inertia and the net section's by about 1 %. This program carries them unrounded. The tee's moment of inertia here is 0.80 in. to the fourth against 0.81 printed, and the dead load deflection 1.63 in. against 1.61 in., on the safe side.
• Tee lateral-torsional buckling moment in Example 4.4. The example takes the tee's depth at the critical section and its torsional constant at the center of the opening. This program takes both at the critical section. The critical moments are about 7 % higher here. They do not govern: the yield moment is several times lower in this example, and the strength matches.
• Top tee Vierendeel moment in Example 4.4. The example's table prints 92.4 kip-in. at the first opening. The net shear and the tee areas it states give about 91 kip-in., which this program gets. The moment is 1.4 % lower than printed and the largest ratio of the top tee about 0.62 against 0.631, within the tolerance. Neither governs the beam.
• Torsional constant of the tees in Example 4.3. This program takes the tee's torsional constant from thin rectangles, with the flange's end correction. The example's values, 0.266 and 0.685 in. to the fourth, come from a method it does not state and are about 1 % higher. The tee's critical moment is very sensitive to this constant. The critical moments are 1 % to 3 % lower here, on the safe side. They do not govern: the yield moment is several times lower in this example.
• Gross section shear in the Example 4.4 summary. The example works out the shear at the gross section as 51.5 kips, then its summary divides the 44.1 kips net of the deck. This program uses 51.5 kips, as Example 4.3 does. The ratio is 0.236 here against 0.202 printed, on the safe side.
• Limiting length of a runway beam with a cap channel. AISC Design Guide 7 Example 14.1.3 uses Section F5 of the specification with a limiting length of 457 in. from its Table A-2. That number is Equation F4-8; Section F5 sets it by Equation F5-5, which gives 407 in. This program follows F5 and reproduces 457 in. by F4-8 as a separate value. The lateral-torsional buckling moment is about 5 % lower than printed, on the safe side, and the biaxial ratio about 0.02 higher. The example passes either way.
• Rounding in the crane runway examples. AISC Design Guide 7 Example 14.1.1 rounds the web slenderness ratio to 1.28 before cubing it (it is 1.276), so its web sidesway strength is 185 kips and 105 kips available, against 183 and 104 kips here. Example 14.1.3 rounds 3,470 / 1.67 to 2,100 kip-in. (2,078; the plastic modulus from the two shapes is 68.9 in.³ against 69.3). About 1 % on these values, lower here. Nothing else follows from them.
• Lower limit of the vertical spectrum in a FEMA example. ASCE 7-22 Equation 11.9-4 says the vertical value shall not be less than half of the horizontal value divided by the direction factor. FEMA P-2192 Table 3-2 does not apply that limit at 1, 1.5 and 2 seconds, where it governs. ILX Calcs applies the limit as the code says, so its values there are higher than printed: 0.449 against 0.425, 0.313 against 0.242 and 0.232 against 0.155 g. The other 20 periods agree within 1 %.
• Footing and soil weights in a strap footing example. The ASDIP example does not state the soil weight, and its screen shows the water table at the surface. The weights of the footings and soil under its pressures are therefore not known. This run uses 110 pounds per cubic foot for soil and 150 for concrete. The pressures come out up to about 6 % higher than the example's rounded values. The difference between the high and the low side of each footing, which the moment alone sets, agrees. ILX Calcs does not change an input to match.
• Maximum stability coefficient under ASCE 7-22. FEMA P-1051 is written to ASCE 7-10 and gets a maximum stability coefficient of 0.091 from a deflection factor of 5.5. ASCE 7-22 adds that this maximum need not be taken less than 0.10. ILX Calcs uses 0.10 here, about 10 % above the printed value, as the edition it follows says. The ratio from the equation itself agrees with the book.
• Stability coefficient printed in a one-story example. FEMA P-1051, Example 9.1, prints a stability coefficient of 0.069 from a load of 888 kips, a drift of 4.51 in., a shear of 179 kips and a height of 32.375 ft. Those numbers give 0.058. ILX Calcs reports what the numbers give, on the 34.25 ft ridge height the example uses for its drift limit: about 0.054. The value and the printed one are both under the limit, so the conclusion in the book does not change.
• Column stability factor rounded in a stud wall example. The HUD guide, Example 5.4, rounds the column stability factor to 0.35 before finding the allowable compression stress of 426 psi. Unrounded it is 0.355. ILX Calcs does not round, so its allowable stress is 433 psi, about 1.6 % higher than printed. The same example's other compression value agrees within 1 %.
• System factor of a stud wall example. The HUD Residential Structural Design Guide, Example 5.4, raises the allowable bending stress of a sheathed stud wall by its own system factor of 1.5. The NDS 2024 has only the repetitive member factor of 1.15. ILX Calcs follows the NDS, so its allowable bending stress is lower than the example's. The bending stress, the Euler stress and the compression values of the example agree within 1 %.
• Uplift case of a ridge beam example. The HUD Residential Structural Design Guide, Example 5.8, subtracts a wind uplift of 102 pounds per foot from a dead load of 121 pounds per foot and rounds the net to 19 before finding the shear and moment. The unrounded net is 18.6. ILX Calcs does not round, so its shear and moment in that small uplift case are about 2 % lower than the printed 124 pounds and 401 pound-feet. The gravity case of the same example agrees within 1 %.
• System factors of a header example. The HUD guide, Example 5.5, raises the allowable bending stress of a double header by its own system factors of 1.3, 1.05 and 1.8, and the allowable shear by a shear stress factor of 2. These come from the guide's tables and an older NDS: the NDS 2024 has only the repetitive member factor and no such shear factor. ILX Calcs follows the NDS and applies none of them, so its allowable stresses are lower than the example's and a header sized by the guide can fail in ILX Calcs. The moments, shear, bearing stress and deflection of the example agree within 1 %.
• Acceleration coefficient at one level of a six-story example. FEMA P-2192-V1 Section 7.5.2 interpolates the coefficient at level 6 between its values at 57.6 ft and 72 ft, but divides by 12 ft, the story height, where the span between those heights is 14.4 ft as in ASCE 7-22 Figure 12.10-2. It gets 0.60 and a force of 471 kips; the figure gives 0.58 and about 457 kips. ILX Calcs follows the figure, so its force at that level is about 3 % lower than the example's. The other five levels agree.
• Last row of a shear wall load table. FEMA P-2192-V1 Table 4-8 prints 6,460 kips for the combination with the earthquake effect added and -378 kips with it subtracted. The two rows differ by twice the earthquake effect, which the text gives as 3,385 kips, so their difference should be 6,770 kips; the table's is 6,838 kips. With the same inputs as its other rows ILX Calcs gets -308 kips. Only that table row differs, by 70 kips. The other two rows that can be checked agree within 0.1 %. The table does not list its dead and live loads, so they were worked back from its first two rows.
• Bolt group coefficient at 75 degrees, 6 in. pitch, 2 in. eccentricity. In every coefficient table of the 16th Edition Manual (Tables 7-6 to 7-13), the row for a load at 75 degrees, 6 in. pitch and 2 in. eccentricity prints values for the larger groups up to about 2 % above the instantaneous center method, and some are printed the same for different gages. Every other value read agrees within 1 %. Example: Table 7-10, 9 bolts per row, prints 26.4; the method gives 25.85. The page images confirm the printed values, and the Manual errata checked as of April 2026 do not list them. ILX Calcs reports the lower value computed by the method, so the result is on the safe side by up to about 2 % at these few table cells.
• Gust-effect factor of the ASCE 7-22 commentary example. ASCE 7-22 Commentary Table C26.11-1 lists G = 0.860 for its rigid-building example, but Eq. 26.11-6 with the table's own turbulence intensity (0.201) and background response (Q² = 0.616) gives 0.818. ILX Calcs computes 0.818 and matches every other value of the table (z̄, Iz̄, Lz̄, Q²). None on designs: the program applies Eq. 26.11-6 as written; the commentary value is 5 % higher.
• Effective moment of inertia: ACI 318-14 examples vs ACI 318-19. The StructurePoint beam and slab examples are written to ACI 318-14, which computes the effective moment of inertia with Branson's expression Ie = (Mcr/Ma)³Ig + [1 − (Mcr/Ma)³]Icr. ACI 318-19 Table 24.2.3.5 replaced it with Ie = Icr / [1 − ((2/3)Mcr/Ma)²(1 − Icr/Ig)], which gives a lower stiffness when Ma is close to Mcr. ILX Calcs uses the 318-19 expression; Mcr, Icr and Ig match the examples, and Ie agrees within 1 % where Ma is well above Mcr. Deflections of lightly cracked members are larger (more conservative) than the 318-14 values: 5 to 16 % in these examples.
• Radius of gyration for the slenderness check. ACI 318-19 6.2.5.2 permits the radius of gyration as r = √(Ig/Ag) or as 0.3 times the dimension in the direction of stability (0.25D for circles). The StructurePoint example uses √(Ig/Ag) = 4.91 in. for a 17 in. square column; ILX Calcs uses 0.3h = 5.10 in., so k ℓu/r is 22.6 instead of 23.5. k ℓu/r is about 4 % lower for a square section; both values are permitted by the code and both are below the limit of 34 in the example.
• One-way shear strength of members without shear reinforcement: ACI 318-14 examples vs ACI 318-19. ACI 318-14 Eq. 22.5.5.1 gives Vc = 2λ√f'c bw d. ACI 318-19 Table 22.5.5.1 changed it for members with less than Av,min (slabs, footings, walls): Vc = 8λs λ ρw^(1/3) √f'c bw d, with the size effect factor λs = √(2/(1 + d/10)), at most 1, and the longitudinal reinforcement ratio ρw. ILX Calcs applies ACI 318-19; the 318-14 examples show the older, higher value. For lightly reinforced slabs (ρw about 0.3 %) Vc is roughly 40 % lower than the 318-14 value: the 318-19 design is more conservative.
• Size effect in two-way (punching) shear: ACI 318-14 examples vs ACI 318-19. ACI 318-19 Table 22.6.5.2 multiplies the two-way shear stress vc by the size effect factor λs = √(2/(1 + d/10)), at most 1, (22.5.5.1.3), which ACI 318-14 did not have. For the 12.75 in. effective depth at the drop panel λs = 0.938, so vc is 265 psi instead of the published 283 psi. ACI MNL-17(21) Two-way Slab Example 1 (p. 108) computes the size effect factor in punching (1.0 at d = 5.63 in.) as ILX Calcs does. Punching capacity of slabs deeper than 10 in. is lower (more conservative) than in the 318-14 example.
• Punching shear around a drop panel: third expression of Table 22.6.5.2. The example's preliminary check around the 10 × 10 ft drop panel uses vc = 4λ√f'c. ACI 318-19 Table 22.6.5.2 (as 318-14) takes the least of 4λ√f'c, (2 + 4/β)λ√f'c and (2 + αs d/bo)λ√f'c; with bo = 514 in. and d = 8.5 in. the third gives 2.66λ√f'c = 188 psi, which governs. ILX Calcs applies the least of the three. ACI MNL-17(21) Two-way Slab Example 1 (p. 108) takes the least of the three expressions of Table 22.6.5.2 (275 psi), as ILX Calcs does. ILX Calcs is about one third lower (conservative); the slab in the example still passes with a large margin (the factored shear stress is about 50 psi).
• Clear span for the minimum thickness of slabs with beams. Table 8.3.1.2, note [2], measures ℓn face to face of the beams. The example uses the clear span between the columns (22 ft − 18 in. = 246 in.) and gets 5.69 in.; with the 14 in. beams the code span is 250 in. and the minimum thickness is 5.79 in. αfm and β match the example. ILX Calcs requires 0.1 in. more; the 6 in. slab of the example satisfies both.
• One-way shear of footings: ACI 318-14 examples vs ACI 318-19. The StructurePoint footing examples (Wight Examples 15-1 and 15-2) use ACI 318-14, Vc = 2λ√f'c bw d. ACI 318-19 Table 22.5.5.1(c) gives Vc = 8λs λ ρw^(1/3) √f'c bw d for members without stirrups (λs may be taken as 1.0 for footings, 13.2.6.2). With the light flexural steel of footings (ρw about 0.25 %) this is about 45 % lower. The factored shear matches the examples; only the strength differs. Under ACI 318-19 both example footings need a few inches more thickness for one-way shear. ACI MNL-17(21) confirms this reading for footings (p. 470, Foundation Example 1 p. 479 and Example 2 p. 491): Table 22.5.5.1(c) without stirrups, the size effect factor neglected under 13.2.6.2, and the steel ratio of the flexural bars. ILX Calcs (ACI 318-19) is more conservative than the 318-14 value: a design shear strength of 165 kips instead of 308 kips (square footing) and 55 instead of 96 kips per 10 ft (wall footing).
• Effective depth for one-way shear of a two-layer footing. The example checks one-way shear with the average effective depth of the two bar layers (28 in.). ILX Calcs uses the effective depth of the bars spanning in the direction checked (28.5 in. for the bottom layer, 27.5 in. for the upper layer, each direction checked), as ACI 318-19 22.5 defines d for the section considered. The critical section moves by 0.5 in., so the factored shear is 1.6 % lower in the bottom-layer direction and 1.7 % higher in the other. Negligible; ILX Calcs checks both directions with their own d, so the governing (upper-layer) direction is covered.
• Development length: simplified table vs general equation. The example takes ℓd from the simplified expressions of ACI 318-14 Table 25.4.2.2 (54.8 in. for a #8 bar). ILX Calcs uses the general Eq. 25.4.2.4(a) of ACI 318-19 with the confinement term (cb + Ktr)/db = 2.5 (3.5 in. cover to the bar centre, 12.7 in. spacing), which the code permits for every case and which gives 32.9 in. ILX Calcs requires a shorter, code-permitted length; the 55 in. available beyond the column face satisfies both.
• Punching at an edge column close to the long edges of a combined footing. With the footing thickened to 40 in. (d = 36.5 in.), the side faces of the 24 in. exterior column are 36 in. from the long edges of the 8 ft footing, which is less than d. ILX Calcs then also checks the critical section that runs to those edges (ACI 318-19 Fig. R22.6.4.3, 'regard as free edge'), and that two-sided section governs (factored shear stress 243 psi). The example checks only the three-sided section (157 psi); the program matches that value for the 36 in. footing, where the sides are farther than d from the edges. ILX Calcs is more conservative for columns within d of a footing edge: here it asks for more thickness than the example.
• Size effect in two-way shear of pile caps: ACI 318-14 example vs ACI 318-19. ACI 318-19 Table 22.6.5.2 multiplies vc by the size effect factor λs = √(2/(1 + d/10)), 0.745 for d = 26 in. Section 13.2.6.2 lets footings and mats neglect it, but not pile caps, so ILX Calcs applies it. The ACI 318-14 example has no size effect: a design shear strength of 947 kips at the column instead of 706 kips. The factored shear of 684 kips matches. ACI MNL-17(21) Strut-and-tie Example 5 (Vol. 2 p. 249) applies the size effect to the two-way shear of a pile cap as ILX Calcs does: 0.636 at d = 39.5 in., vc = 161 psi (tested). ILX Calcs (ACI 318-19) is about 25 % more conservative in two-way shear; the example's 33 in. cap still passes (684 kips of factored shear against 706 kips of strength).
• Pile-cap one-way shear: weight of the cap and rounding of the pile share. For piles 1 in. inside the critical section, ACI 318-19 13.4.6.5 counts a linear share of the reaction, 5/12 of 114 kips = 47.5 kips; the example rounds it to 48 kips and takes a factored shear of 96 kips, ignoring the cap weight. ILX Calcs includes the cap weight in the pile reactions and subtracts the factored weight of the cap beyond the section: 93.7 kips. ACI MNL-17(21) has no pile straddling a one-way section: in its pile cap (Strut-and-tie Example 5, Vol. 2 p. 249) every pile lies inside the section and gives no shear under 13.4.6.5, and the example neglects the cap weight by its statement. 2.4 % lower shear than the rounded published value, 1.4 % lower than the unrounded one; both follow from statics with the cap weight.
• Axial load term in the one-way shear of a retaining-wall stem. ACI 318-19 Table 22.5.5.1(c) adds Nu/(6Ag) to the shear stress for axial compression. The example counts the stem's own weight above the base (Nu = 3.08 kips per foot, +2.7 psi) and gets a design shear strength of 10.98 kips per foot. ILX Calcs neglects Nu (permitted, conservative) and gets 10.67 kips per foot with the same λs = 0.92 and ρw. ILX Calcs is 3 % more conservative in stem shear.
• Bearing length of DG1 Example 4.7-12 from rounded intermediate values. AISC Design Guide 1 Example 4.7-12 solves Eq. 4-65 as Y = 17.5 in. − 17.2 in. = 0.300 in., subtracting two numbers rounded to 0.1 in.; the unrounded terms (f + N/2 = 17.5 in., square root 17.226 in. for LRFD and 17.253 in. for ASD) give Y = 0.274 in. (LRFD) and 0.247 in. (ASD). With Eq. 4-63 the rod tension is then 111.5 kips (LRFD) and 66.9 kips (ASD) instead of the published 113 and 68.4 kips. ILX Calcs uses the unrounded values; qmax (42.0 and 27.9 kips/in.) matches the Example. Rod tension 1.3 % (LRFD) and 2.2 % (ASD) lower than the rounded published values; the bearing length is a fraction of an inch either way and does not change the plate design.
• Partially grouted wall as an equivalent thickness in the TMS shear wall webinar. In Examples SD-2 and SD-3 of the TMS webinar handout (TMS 402-16), the interaction diagram and the maximum reinforcement check treat the partially grouted wall as a solid wall of equivalent (averaged) thickness, 3.39 in. for grout at 48 in. ILX Calcs takes the compression zone as the face shells plus the grouted cells, as the TMS 402 Commentary to the maximum reinforcement provision describes. The published 0.9 Pn at the maximum reinforcement strain is 323 / 364 kips (ILX 354 / 393 kips) and the wall of SD-2 is stressed to 94 % of its flexural design strength (ILX 89 %). The net shear area, the shear strengths and the neutral axis depth agree. ILX gives a larger compression block in the partially grouted wall: 8 to 10 % more axial capacity at the maximum reinforcement strain and 6 % more flexural strength in these examples. The FEMA P-1051 example (face shells plus grouted cells, as ILX) agrees within 0.2 %.
• Flexural strength of the FEMA pilaster with one bar layer. FEMA P-1051 Section 13.1.6 computes the flexural strength of the 16 in. square pilaster with the two tension bars only (design moment strength 520,059 lb-in., 43.3 kip-ft). ILX Calcs solves the strain compatibility with all four bars, and the two bars nearer the compression face are also in tension at that neutral axis. ILX gives a 2 % higher flexural strength than the simplified published value; the pilaster passes either way.
• Anchor bolt steel strength from the tensile strength. The TMS handout of March 2018 is written to TMS 402-16, which takes the steel strength of an anchor bolt from its yield strength, 36 ksi in that handout. TMS 402-22 takes it from the specified tensile strength, 60 ksi for an A307 bolt, with a lower strength reduction factor. ILX gives a higher steel strength than the handout: 25 to 34 percent at the sizes in these examples. Where masonry governs there is no change.
• Masonry crushing coefficient of anchor bolts in shear. CMHA TEK 12-03C is written to the 2013 code, whose masonry crushing strength has a coefficient of 1,050. The 2016 code raised it to 1,750, 67 percent higher, as the TMS handout of March 2018 explains. ILX uses 1,750, taken as kept in the 2022 code. ILX gives 67 percent more crushing strength than this TEK. The TEK's design passes under either value.
• Cracked moment of inertia with bars off the wall centre line. The TMS handout of 2021 uses the 402-16 equation, which multiplies the axial load term by half the thickness over the depth. TMS 402-22 Equation 9-28 places the axial load at the wall centre line, a separate term. They are equal for bars at the centre and differ for bars at the faces. ILX gives a cracked inertia and buckling load about 4 percent lower than the handout; the moment magnifier moves by less than 1 percent.
• Quick check of the deflection of the pier. The TMS handout checks the 28 ft pier quickly, with the lateral load of the wall above the door over the whole height and the cracked section throughout, and says the detailed calculation is in the Guide. ILX puts the load on the part of the height where it acts and uses the uncracked section up to the cracking moment. ILX gives a much smaller deflection than the quick check, which the handout shows as a conservative bound. Both pass the limit.
• A rounded load in the FEMA pier. FEMA P-1051 prints 1,200 plf for a load of 0.4 × 1.43 × 103 psf × 20 ft, which is 1,178 plf. ILX uses the 58.92 psf that the equation gives. ILX's top reaction is 2 to 3 percent lower than printed. Strength at the door head agrees.
• Axial load in the flexural strength of the FEMA pier. FEMA P-1051 computes the compression force as the steel force plus the factored axial load (and prints 184.1 kips where its own numbers add to 186.1). ILX, like the TMS handout of the same pier, finds the nominal moment at the nominal axial load, the factored load divided by the strength reduction factor. ILX gives a nominal moment 1.5 percent higher than FEMA. The TMS handout's values for the same wall agree with ILX within 0.1 percent.
• Deflection of the FEMA pier. FEMA P-1051 checks the pier with the cracked section over the whole height, and says this is a conservative check. ILX uses the uncracked section up to the cracking moment, the code's two-part form, along the height. ILX gives a smaller deflection than the conservative FEMA check. Both pass the limit.
• Pilaster flexural strength with one bar layer in FEMA P-1051. FEMA P-1051 Section 13.1.6 computes the flexural strength of the 16 in. square pilaster with the two tension bars only (stress block depth 2.11 in., design moment strength 520,059 lb-in., 43.3 kip-ft). ILX Calcs solves the strain compatibility with all four bars: the other two bars, 3.6 in. from the compression face, sit below the neutral axis (3.1 in. deep) and add tension, so the design strength is 44.3 kip-ft. The TMS night school column example makes the same comparison (47.3 kip-ft with two bars, 48.8 kip-ft with both layers) and ILX matches its both-layer value within 0.2 %. ILX gives a 2 % higher flexural strength than the simplified published value; the pilaster passes either way. The stiffness values of the example (gross and cracked moment of inertia, cracking moment) agree within 0.1 %.
• Cold work of forming in the SSMA allowable moments. The SSMA Product Technical Guide includes the strength increase from the cold work of forming (AISI S100 Section A7.2) in the allowable moments marked with its footnote 2, such as 30.33 kip-in. for the 600S162-54 at 50 ksi. ILX Calcs uses the specified yield stress without that increase. ILX is lower (conservative): 27.80 kip-in. for the 600S162-54 at 50 ksi. Sections without the footnote agree within 0.3 %.
• Effective section modulus of the 600S162-54 at 50 ksi in the SSMA guide. The SSMA guide lists Sxe = 0.916 in.³ for the 600S162-54 at 50 ksi. The AISI S100 effective width procedure (flange with its edge stiffener, lip reduced by RI, web under stress gradient) gives 0.928 in.³, both in ILX Calcs and in the independent hand calculation of example CS-4. The SSMA program details are not published; the other sections compared (600S162-33, 800S162-43, 800S162-54, 1000S162-54) agree within 0.3 %. The narrow 362S162 sections differ more (362S162-54 at 50 ksi: 0.444 in.³ listed, 0.468 in.³ by S100) and are not used as examples. ILX is 1.4 % higher than the guide for this section.
• Beam stability factor of the AWC TR 14 ridge beam example. AWC Technical Report 14 Example 3.1 (2-1/2 × 21 24F-V4 glulam braced by joists at 4 ft) takes CL from the report's own buckling-moment method (Mcr = 1.3 Cb Ce E'y05 Iy / lu), giving CL = 0.88 and M' = 37,250 ft-lb. ILX Calcs applies NDS 2024 3.3.3: effective length le = 2.06 lu from Table 3.3.3, RB = 18.2 and CL = 0.857 (M' = 36,200 ft-lb). The NDS values the report also uses (Fbx* = 2,760 psi, CV = 0.9871, M = 36,750 ft-lb) agree. The program is 2.8 % lower (conservative) than the TR 14 method for this beam; NDS 3.3.3 is the method of the code.
• Lower bound of Cs in the FEMA P-2192 coupled-wall example. FEMA P-2192-V1 Section 4.5.1.7 writes the lower bound 0.044 SDS Ie but evaluates it with 0.65 g (the SD1 of the example) instead of SDS = 1.10 g, giving 0.029. ASCE 7-22 Eq. 12.8-6 with SDS = 1.10 g gives 0.0484, which ILX Calcs computes. None on the result: the governing Cs (0.048, the long-period limit) and the base shear (2,090 kips) agree with the example.
• Base shear of the FEMA P-2192 composite plate shear wall example. FEMA P-2192-V1 Section 5.5.3.6 multiplies Cs rounded to 0.048 by W = 25,844 kips (its Table 5-4 sums to 25,855 kips). ILX Calcs keeps the unrounded Cs = 0.044 SDS = 0.04844 (Eq. 12.8-6 governs) and W = 25,855 kips, so V, the story forces and the overturning moment are 1.2 % higher; the period, k and the distribution factors Cvx agree. The program is 1.2 % higher (conservative) than the example.
• Plastic modulus of the deep UPE channels. The steel catalog prints the weak-axis plastic modulus of a UPE 400 as 191 cm³. A hand calculation from its dimensions gives 220 cm³ (the plastic axis lies inside the web; web part 400 mm × 11.3 mm and 2.2 mm, flanges 3,654 mm² at 52.9 mm), and ILX Calcs gives 220.8 cm³ with the fillets. UPE 360 (178 printed, 189 calculated) and UPE 330 (156, 162) show the same difference; the smaller sizes agree. The catalog's value looks low. ILX Calcs reports the value from the geometry.
• Surface perimeter PA of some HP shapes. The AISC Shapes Database v16.0 lists PA of about 3 to 4 for eight HP12 and HP14 rows, where the same rows' PB is about 70 to 85 in. and every other HP row's PA is close to PB minus the flange width. ILX Calcs calculates 58 to 70 in. These database entries look wrong. They affect paint and fire-protection quantities only, no strength.
• Area of the lightest M shapes. For a few M shapes the AISC database's area, its nominal weight and its fillet dimension do not agree: M3X2.9 lists 0.914 in.², while 2.9 lb/ft is 0.853 in.² of steel. The database's fillet distance is also too large for the weight on 14 of the 16 M shapes and on 3 HP shapes. ILX Calcs takes the fillet that closes the weight on those rows and says so on the row. Area and strong-axis properties of those rows are up to 7 % below the database's. The rows are flagged.
• Flange slope of MC channels. The AISC database does not list the flange slope of MC channels, and it varies by shape. ILX Calcs uses 1:12, or 1:6 for MC13 and for flange thickness up to 0.32 in., a rule read from the published weak-axis inertias. Those values therefore are not an independent check for MC, and they still differ by up to 8 %. Weak-axis values and torsion terms of MC channels are less certain than other families. The rows are flagged.
• Area of some standard pipes. For some pipes the AISC database's area differs from the area of its own diameter and design wall: Pipe20XS lists 27.6 in.² where the listed 20 in. and 0.465 in. give 28.5 in.², Pipe10STD lists 11.5 where the listed values give 11.1. The cause was not found. Up to 3.4 % on area and inertia of those rows. ILX Calcs reports the value from the geometry.
• Radius of gyration of track 1000T250-54. The SSMA guide prints a radius of gyration of 3.577 in. for this track, while its own inertia and area give 3.757 in., as ILX Calcs does. Two digits look swapped. None on results: ILX Calcs reports the value from the geometry.
• Published torsion constants disagree between sources. Catalogs print different torsion constants for the same shape: for the lightest HEAA shapes the sources differ from the true-outline value by up to 13 %. ILX Calcs solves the torsion on the true outline with fillets, and that solution agrees with an independent program within 0.03 %. Compare torsion constants with care against a catalog. Results from ILX Calcs are for the geometry shown.
• Warping and torsion basis: true outline and thin-walled. AISC and SSMA tabulate the warping constant, the shear center and related terms from a centre-line model without fillets. ILX Calcs reports those and also the value on the true outline. For a thick tapered channel they differ a lot: C10X20 is 56.9 in.⁶ in the database and 44.7 in.⁶ on the true outline, with the shear center 0.64 and 0.49 in. from the web. The centre-line values match the database within about 1 %. AISC 360's equations assume the centre-line values, so a module adopting this database would use those. The engineer chooses.
• Minor principal moment of inertia of a rolled angle. Rolled angles have rounded leg toes, whose radius the AISC Shapes Database does not list. ILX Calcs draws them with half the root radius, a single assumption chosen across the whole angle family. For L4X4X1/2 the area, the moment of inertia about the leg, the centroid and J all match within 1 %, but the minor principal moment of inertia comes out at 2.28 in.⁴ against the tabulated 2.25 in.⁴, 1.5 % higher. With square toes it was 3 % higher. The minor principal value of a rolled angle is about 1.5 % high; use the database value for single-angle design if that matters.
• Moment distribution stopped after two cycles. Example 12.3 of Udoeyo's Structural Analysis distributes the moments for only two cycles with distribution factors rounded to 0.01, so the column moments are not converged: the printed column moments MBD = 14.94 and MDB = 7.47 kip-ft against the exact stiffness solution 15.09 and 7.55 kip-ft (1.0 % apart). The beam moments of the same example match within 0.4 %. None: the program gives the exact elastic solution.
• Second-order drift printed below a rigorous solution. AISC Design Examples C.1A and C.1B print a second-order drift of 0.290 and 0.204 in. (LRFD), a ratio to the first-order drift of 1.60 and 1.41, and 1.66 and 1.44 under ASD. ILX Calcs gets the printed first-order drifts within 0.3 %, with shear deformation, and the printed moments, shears and axial forces within 0.4 %, but its second-order drifts are 2.5 to 4 % higher, with ratios of 1.64 and 1.45 (LRFD), 1.71 and 1.50 (ASD). The printed 1.41 is below what sway alone gives for those loads, 1.43, by the story stiffness relation the examples use themselves. The same solver reproduces the AISC Commentary benchmark drifts within 0.4 % and the closed-form solutions within 0.05 %. The difference is inside the 5 % the Commentary allows for deflections. The drift ratio read against a limit is a little higher than printed, on the conservative side: example C.1A under ASD reads 1.71 against the 1.7 for gravity-only imperfections, and C.1B under ASD reaches the 1.5 limit. Moments and forces in these examples are not affected, because the only sway load is small.
• First-order moment not equal to shear times height. Figure C.1C-3 of AISC Design Examples prints 5.32 kips of shear at the pinned base of column B and 108 kip-ft at its top. In a first-order analysis of a 20 ft column pinned at the base the moment is the shear times the height, 106.4 kip-ft, which is what ILX Calcs reports. Column C agrees: 6.53 kips gives 130.6 against the printed 131. None: the program reports the statically correct moment.
• Story buckling strength from a rounded story shear. Example C.1C under ASD takes the story shear as 4.35 minus 3.55 kips, 0.800 kip, where the lateral load is 0.806 kip, and gets a story buckling strength of 875 kips. ILX Calcs keeps the unrounded shear and gets 886 kips, 1.2 % higher. The sidesway amplifier from it matches the printed 1.54 within 0.3 %. None on the verdict: the first-order method still reads not permitted under ASD, as the example says.
• Design Guide 28 warehouse: our model of one line of the building. Design Guide 28 Example 3.2 reports forces and drifts from a model it does not print. We reconstructed one column line: one eleventh of the building's gravity and wind, the two end beams with their own 40 ft of roof, nine pinned columns taking the rest. The axial forces agree within 0.6 % and the column moment at the top of the governing combination is 10,550 kip-in. against the printed 10,800 (2.3 % low); the drifts under wind agree within 1.6 %. A few values miss the 1 % tolerance: smaller moments that are the difference of two large numbers, up to 7 %, and the drifts under notional load alone, 4 % high. These may come from the reconstruction, for example how the notional load is shared between the lines. Nothing was adjusted to reduce them. The solver itself is checked by the Commentary benchmarks. Treat this example as a cross-check of a whole method on a frame with a large amplification, not as an exact match.
• Joist live load deflection printed as three quarters of an inch. The SJI webinar Properly Specifying Steel Joists (2019, slide 73) scales the 3.86 in. deflection of a 96DLH21 under its red-figure load of 877 plf to a 200 plf live load as 200 / 877 times 3.86 in. and prints 3/4 in. The product is 0.88 in., which ILX Calcs reports; the 3.86 in. limit itself matches. None on designs: the program prorates the red figure exactly, as the load-table note describes; the slide's conclusion (no special deflection note needed) holds either way.
• Design Guide 9 reads the torsion functions from its charts. AISC Design Guide 9 reads the rotation and its derivatives from the graphs of its Appendix B to two digits, and AISC Design Example H.6 reuses those readings. ILX Calcs solves the same differential equation exactly: for example 0.0955 where the guide reads 0.09 in its Example 5.1, 0.481 where it reads 0.46 in Example 5.5. The exact solution was checked separately against closed-form solutions and an independent numerical integration. Values within 3 percent are counted as agreeing; the others are listed here. The program is higher than the guide on most of these values, by up to about 10 percent on a stress that is small to begin with, so it is on the safe side. Compared with a designer reading the charts, results differ by the reading error only.
• Tube torsional shear in Design Guide 9 Example 5.2 uses the whole torque. Example 5.2 divides the whole 90 kip-in. torque by twice the wall times the enclosed area, 1.72 ksi, although a torque at midspan divides equally between the two supports, as the same example assumes when it computes the rotation. ILX Calcs uses the 45 kip-in. each side carries and the torsional constant of the current shapes database, 0.92 ksi. AISC Design Example H.5C uses the torque the same way ILX Calcs does. The guide is about twice as high here (conservative). The strength check itself follows AISC 360-22 H3.1 and agrees with Examples H.5A, H.5B and H.5C.
• Tube torsional constant of 1997 against the current database. Example 5.2 uses a torsional constant of 187 in.4 for the 1997 TS10x6x1/2 tube. The AISC Shapes Database v16.0 lists 176 in.4 for the HSS10X6X1/2 that replaced it, so the rotation is 0.00137 rad against the printed 0.0013 rad. The rotation is about 5 percent larger, on the safe side, and it is small in any case.
• Largest channel shear stress found between the stations the guide checks. Example 5.5 evaluates the channel at the support, at one fifth of the span and at midspan and reports a largest shear stress of 4.35 ksi. ILX Calcs evaluates the whole span and finds 4.72 ksi at 1.4 ft, about one eighth of the span. At the guide's own station it gets 4.36 ksi. The program reports a higher maximum, on the safe side. The guide itself warns that the stresses should be checked at several locations.
• Channel flange shear stresses added as absolute values. At the channel flange points Example 5.5 adds the three shear stresses with their directions and takes no flexural shear at point 1, getting 3.44 and 3.12 ksi at one fifth of the span. ILX Calcs adds absolute values and includes the flexural shear at point 1, getting 4.00 and 4.10 ksi. Higher flange shear stress, on the safe side. In this example the web stress is larger still, so the governing result is not affected.
• Buckling stress in AISC Design Example H.6 exceeds the plastic moment. Example H.6 multiplies the tabulated flexural strength at a bending coefficient of 1.0 by 1.32 and divides by the section modulus, 65.8 ksi for LRFD and 65.9 ksi for ASD. AISC 360-22 Equation F2-2 limits that strength to the plastic moment, which gives 55.3 ksi, the value ILX Calcs uses. The program's critical stress is lower, on the safe side. Yielding under normal stress governs over buckling in the example either way, as the example itself concludes.
• Moments of some C-sections include the cold work of forming. For the sections marked with its footnote 2, the SSMA Product Technical Guide (2022, pages 10 to 13) raises the yield stress for the cold work of forming, as AISI S100 permits, so its local and distortional moments are higher than at the catalog yield stress: 30.33 and 25.90 kip-in. for a 600S162-54 at 50 ksi, against 27.80 and 24.23 here. The program uses the yield stress you enter and adds nothing for cold work. With the raised yield stress worked out from the same table row (55.3 ksi), it gives 30.35 and 25.89 kip-in. The program is lower by about 6 to 11 percent on those sections unless you enter the raised yield stress yourself, as the engineer of record.
• Header deflection taken at the service moment. The SSMA Product Technical Guide (2022, page 56) works out the effective moment of inertia of a section at its allowable moment. AISI S100 Appendix 1 takes the stress at the load being checked, and the program does that, so where deflection governs it is a little stiffer: 286.2 against 283.3 pounds per foot for two 800S162-54 over 12 feet. The program allows about 1 percent more load than the table on rows governed by deflection.
• L-header spans of CFSEI Design Guide 8 (2000). Design Guide 8 prints spans for double L-headers with no calculation, tributary width or snow factor. The comparison assumes a 14 foot tributary width and a roof snow load of 0.7 times the ground snow load, moment limited. With those assumptions, legs up to 8 inches come within 4 percent of the guide. For 10 inch legs the guide's spans are 15 to 18 percent longer: it predates the AISI S240 safety factor of 2.25 for legs over 8 inches, which the program applies. The program gives shorter spans than the guide on 10 inch legs, as the current standard requires. The comparison is a cross-check on assumed loads, not a verification of the method.
• Bare steel strength of the built-up box in Design Example I.7. Design Example I.7 states, without showing the calculation, bare steel strengths of 1,980 and 541 kips for the 30 in. box with 1/2 in. and 1/4 in. plates. Those figures reproduce (1,966 and 540 kips) with the wall factors the Specification gives for HSS and a flat width of the depth less three thicknesses. A box of four plates is not an HSS, so ILX Calcs uses the factors for other stiffened elements and the clear width between plates, as the Specification and the same example's slenderness calculation read, and gets 1,882 and 509 kips. None in this example, where the composite strength governs by a wide margin. In general the program is about 5 to 6 % lower on this bare steel strength, which only matters if it governs over the composite strength; that is on the safe side.
• Bare steel strength of HSS20x20x3/8 in the Steel Tube Institute table. The capacity table of the Steel Tube Institute article Filling the Void (June 2024, p. 6) lists 821 kips for the bare HSS20x20x3/8 at 42 ft. The article's stated A500 wall (design thickness 0.349 in.) gives 730 kips by hand from Section E7, and ILX Calcs computes 729. A 0.375 in. wall, as in ASTM A1085, gives 826 kips, so the table cell probably comes from that wall; this is our inference, the article does not say so. The eight other bare steel values and all eighteen composite values in the table match. None on the composite strength, which governs this section at 1,360 and 1,600 kips and matches the table.
• Corner stress formula against the finite-element results it was fitted to. The corner stress formula of Ioannides, Thompson and Barenberg (1985) is a curve fitted to their finite-element results for a load at the corner of a slab on a dense-liquid subgrade. It reproduces the finite-element stresses of their Table 5.13 within 1 percent for most runs, but the run with the largest loaded area (7.5 in. square on a 9 in. slab) is 2.2 percent below, and the run on the thinnest slab (6 in.) is 1.5 percent below. ILX Calcs applies the published formula as written. Corner stresses can be up to about 2 percent below the finite-element values for large contact areas or thin slabs; the factor of safety covers the difference, or the engineer may choose the Westergaard 1926 corner formula, which gives higher corner stresses.
• Beam on elastic foundation: hand calculation with rounded table constants. The Structville example (a 10 m concrete beam with free ends on soil springs, 300 kN at 3 m) is worked by hand with the coefficients of Roark's tables rounded to four or five digits, and one of them is evaluated at 1.974 instead of the 1.980 the beam's own numbers give. The exact solution of the same beam is 12.39 mm of settlement at the left end (published 12.23 mm) and 231.05 kN-m under the load (published 228.39 kN-m), about 1.2 % apart. ILX Calcs gives the exact values, confirmed by an independent closed-form solution and by its own convergence tests; the stiffness value of the example matches to four digits. The STAAD.Pro check in the same article uses springs 1 m apart and lands lower still (12.20 mm, 228.15 kN-m). None on designs: the program's settlement and moment are about 1 % higher than the rounded hand values.
• Pile deflection in clay: rounded stiffness factor. Example 6.12 of Kouretzis's Fundamentals of Foundation Engineering estimates the deflection at grade of a fixed-head pipe pile in clay with the relative stiffness factor rounded from 0.507 to 0.50 per meter and quotes 0.019 m. With the unrounded factor the same Broms equation gives 0.0199 m, which ILX Calcs reports. The three ultimate lateral loads of the example (short, intermediate and long pile) match within 0.1 %. The program's deflection is 4 % larger than the printed value, on the conservative side.
• Broms chart readings in the FHWA exercise. FHWA HI-97-013 Student Exercise 8 reads the ultimate lateral load and the deflection of a fixed-head prestressed pile in sand from Broms' charts (Figures 9.30 and 9.33): 295 kN and 11 mm. ILX Calcs uses the closed-form equations the charts are drawn from: 280 kN (5 % lower) and 11.2 mm (2 % higher). The passive pressure coefficient of the exercise matches exactly. The program is slightly more conservative than the chart readings: a lower lateral capacity and a larger deflection.
• One-way shear of wall footings: the published formula vs ACI 318-19. The StructurePoint example (Wight Example 15-1, ACI 318-14) and the UET Peshawar lecture take the concrete shear strength as 2 times the root of the concrete strength, times width and depth. ACI 318-19 keeps that form only for members with at least the minimum stirrups. A footing without stirrups uses Table 22.5.5.1(c), which depends on the flexural steel ratio. With the light steel of a footing, at about 0.3 %, the strength is about 40 % lower. The factored shear matches the examples; only the strength differs. ACI MNL-17(21) confirms this reading for footings (p. 470, Foundation Example 1 p. 479 and Example 2 p. 491): Table 22.5.5.1(c) without stirrups, the size effect factor neglected under 13.2.6.2, and the steel ratio of the flexural bars. ILX Calcs is more conservative: 5.5 instead of 9.6 kips per foot on the 13 in footing, which fails under ACI 318-19 and needs more thickness or steel.
• Development length: simplified table vs the general equation. The StructurePoint example uses the simplified table of ACI 318, 21.9 in for a No. 4 bar. The program uses the general equation of 25.4.2.4 with the actual cover and spacing, 13.1 in. Both are permitted. ILX Calcs asks for a shorter, still code-compliant length. The available length of 22 in passes either way.
• Plain concrete flexure at the top of the footing. ASDIP checks the footing top, which has no bars, with a strength factor of 0.55 and the full 12 in thickness, 3.6 kip-ft per foot. ACI 318-19 gives a factor of 0.60 (Table 21.2.1) and takes 2 in off concrete cast against soil (14.5.1.7), so the program gets 2.7 kip-ft per foot. ILX Calcs is more conservative on this check, and it only appears when an overhang loses soil contact.
• One-way shear values of the ASDIP screenshots. ASDIP prints values to one decimal and does not show the shear calculation. On the side near the wall offset it prints a shear of 0.9 kips per foot; the program gets 0.80 at the printed depth of 8.7 in. Its strength of 5.0 kips per foot compares with 4.93 from Table 22.5.5.1(c) with the printed values. The moments on both sides and the shear on the other side match. The reason could not be read from the publication; another effective depth is a possibility, not a finding. ACI MNL-17(21) Foundation Example 2 (p. 491) sets out the method ILX Calcs uses: for a concrete wall the section at d from the face, Vc by Table 22.5.5.1(c) with the size effect neglected (13.2.6.2) and the steel ratio of the flexural bars. The ASDIP difference is not a matter of method. Small: about 11 % on a low shear that governs nothing in the example, and 1.5 % on the strength.
• Reduction of development length for excess steel. With the optional reduction of 25.4.10, ASDIP takes the required steel from the moment alone, which brings the length down to the 12 in minimum. The program takes the required steel as the larger of the steel for the moment and the minimum steel, and gets 13.7 in. ILX Calcs is slightly more conservative when you choose this option. Without it no reduction is taken.
• Critical sections under a masonry wall. CE-Ref Example 10 takes the moment at the face of the masonry wall and the shear at a quarter of the wall thickness inside the face, without adding the effective depth. ACI 318-19 Table 13.2.7.1 takes the moment halfway between the center and the face, and 13.2.7.2 measures the shear section from there, at the effective depth. The factored pressure and the depth match. ACI MNL-17(21) Foundation Example 2 (Figs. E2.2 and E2.3, pp. 491 and 492) draws the sections as ILX Calcs takes them: under a masonry wall the moment section halfway between the center and the face, and the shear section at d beyond that line. The moment is higher than published (1.78 instead of 1.27 kip-ft per foot) and the shear stress is lower (20 instead of 40.5 psi).
• Shear strength in the CE-Ref example. CE-Ref Example 10 uses a concrete strength of 2,500 psi in the shear formula although the example gives 3,000 psi, and the ACI 318-05 formula. The program uses Table 22.5.5.1(c) of ACI 318-19 with 3,000 psi and the example's light steel. ILX Calcs is more conservative: about 39 instead of 75 psi.
• Steel along the wall in the CE-Ref example. CE-Ref Example 10 uses a ratio of 0.002 on a depth of 8.75 in, which is not the 10 in thickness of the footing. ACI 318-19 24.4.3.2 gives 0.0018 on the gross section. ILX Calcs asks for 0.54 instead of 0.525 square inches, 3 % more.
• Snow density of the ASCE 7-22 commentary drift example. Example 3 of the ASCE 7-22 snow commentary puts the drift on a lower roof whose ground snow load is 32 psf, but it computes the snow density from the upper roof's 40 psf (19 pcf instead of 18.2 pcf) and divides the lower roof's balanced load by it. Its windward drift height (4.55 ft before the three-quarter factor) also does not follow from Eq. 7.6-1 with its own inputs, which give 4.69 ft with 19 pcf and 4.79 ft with 18.2 pcf. ILX Calcs uses the density of the roof the drift sits on. The flat roof loads, the clear height, the drift surcharge (65.3 against 64.8 psf) and the peak load at the step (92.2 against 92 psf) agree within 1 %. Drift heights about 4 to 5 % higher and drift widths about 5 % wider than the example; the peak drift load at the step is the same within 1 %.
• Wall anchorage force below the code minimum in a low-seismic example. The FEMA P-1051 five-story masonry example (SDC C, design spectral acceleration 0.37 g, rigid plank diaphragm) reports a wall anchorage force of 61.6 lb per foot from the basic anchorage equation alone. ASCE 7-22 12.11.2.1 also requires at least 0.2 ka Ie times the tributary wall weight (and ASCE 7 1.4.4 asks for 0.2 times the wall weight in every category), which is 83.2 lb per foot here. ILX Calcs reproduces the 61.6 lb per foot equation value and applies the minimum. Wall anchorage forces at low seismic accelerations (where 0.4 times the design acceleration is below 0.2) are 35 % higher than the published value: the code minimum governs.
• Basement wall strength at the combination with the least axial load. The ACI E702.4 example checks the wall base only under 1.2 dead + 1.6 live + 1.6 earth pressure and quotes a design moment strength of 31.6 kip-ft per foot (spColumn) at that axial load. The program checks every ASCE 7-22 strength combination; under 0.9 dead + 1.6 earth pressure the wall carries less axial compression, so its moment strength is lower (30.4 kip-ft per foot) while the earth pressure moment is the same. At the example's own axial load the program gives 31.64. Conservative: the governing combination gives a 4 % lower strength than the example's single check.
• Corbel flexural steel with an approximate lever arm. The VCmaster corbel worksheet finds the flexural steel with a lever arm of 0.9 times the effective depth. ILX Calcs solves the rectangular stress block exactly (ACI 318-19 22.2), which gives 0.62 square inches instead of 0.67 for this corbel. Every other value of the worksheet matches. None on this design: the primary steel is governed by two thirds of the shear-friction steel plus the axial steel, which both methods give alike.
• Corbel flexure with the beam strength reduction factor. The Maple Flow corbel worksheet uses a strength reduction factor of 0.90 for the flexural steel. ACI 318-19 Table 21.2.1 row (f) gives 0.75 for every action of a bracket or corbel, so ILX Calcs finds 0.450 square inches instead of 0.373. None on this design: the primary steel is governed by the shear-friction requirement. Where flexure governs, ILX Calcs asks for more steel than the worksheet.
• Corbel shear limit of older ACI editions. The Maple Flow corbel worksheet, although labelled ACI 318-19, limits the nominal shear to 800 psi times the width times the depth, the limit of ACI 318-08 and earlier. ACI 318-19 16.5.2.4 limits it to the least of 0.2 f'c, 480 + 0.08 f'c and 1,600 psi; for this 5,000 psi corbel that is 880 psi, so the design limit is 198 kips instead of 180 kips. ILX Calcs uses the 318-19 limit (also tested). ACI MNL-17(21) designs its corbels by strut-and-tie (Strut-and-tie Examples 3 and 4) and does not apply 16.5.2.4. It applies the same three expressions to shear friction under 22.9.4.4 in Diaphragm Example 3 (p. 380): 800 psi at 4,000 psi, where 0.2 f'c and 480 + 0.08 f'c coincide. The program allows about 10 % more shear than the worksheet for this corbel, as ACI 318-19 permits.
• Closed ties from the required or the provided primary steel. ACI 318-19 16.5.5.2 requires closed ties of at least half of the primary tension steel less the axial-force steel, where the primary tension steel is the area of the bars in the corbel. ILX Calcs uses the area provided (1.80 square inches here); the Maple Flow worksheet uses the area required (1.735), so it asks for 0.423 square inches of ties against 0.456. The program asks for up to a few percent more ties than a design based on the required steel (conservative).
• Printing errors in the TMS Masonry Designers' Guide 2022 lintel example. Example 12.4-2A of the Guide (the free sample, written to TMS 402-22) has printed numbers that its own equations do not give. For two No. 4 bars it prints a reinforcement ratio of 0.00092; that is the ratio of the one No. 5 bar tried before them, and two No. 4 bars give 0.00119 (the 2021 TMS handout of the same beam prints 0.00119). In the rework it prints 1,640,000 lb-in. as the nominal moment of four No. 4 bars; by hand the nominal moment is 1,826,000 lb-in. and 0.9 times that is 1,643,000 lb-in., so the printed number is the design strength. Two smaller slips are within the test tolerance or have no effect: the nominal moment of two No. 4 bars is printed as 1,038,000 lb-in. where the arithmetic gives 1,032,000 lb-in., and the page writes 0.007 times the width where it means 0.0007 (its result, 0.0053, is right). ILX Calcs computes the values the equations give. None on designs. The example's conclusions all hold: one No. 5 bar fails the minimum reinforcement, two No. 4 bars pass, and four No. 4 bars in two courses pass the maximum.
• Maximum reinforcement of a beam: the 2016 limit in the older TMS examples. The TMS strength design beam example (webinar handout, Example 6.3.1.8, TMS 402-16) compares the reinforcement with a maximum ratio of 0.00952, the 2016 rule with the extreme bar at 1.5 times its yield strain. TMS 402-22 replaced it: a beam must be tension controlled, with the net tensile strain at least the yield strain plus 0.003. For Grade 60 bars in concrete masonry at a specified strength of 2,000 psi the limit is 0.00711, the value TMS prints in its 2022 handout and in the 2022 Designers' Guide. ILX Calcs uses the 2022 limit. The largest amount of reinforcement allowed in a beam is about 25 % lower than the 2016 example shows. This example's beam is far below either limit.
• Depth used for the stirrups in the 2017 TMS beam example. The 2017 TMS strength design handout finds the stirrup area of its 24 in. deep beam with the effective depth of 20 in. in the steel shear strength, and asks for 0.101 square inches at 8 in. The 2021 TMS handout and the 2022 Designers' Guide use the actual depth of the beam there (48 in. for their 48 in. beam, with 40 in. only in the shear area). ILX Calcs follows the later examples, which gives 0.084 square inches for this beam. The shear area, the masonry shear strength, its upper limit and the steel strength the beam needs all agree with the handout. About 17 % less stirrup area than this one handout asks for, the amount the 2021 and 2022 TMS examples would give. The spacing limits use the same depth.
• Lintel span rounded to 5.7 ft in the NCMA TEK example. The NCMA TEK 17-1D example finds the effective span of 5.67 ft (5 ft 4 in. plus 4 in.) and then computes its moments and shears with 5.7 ft. ILX Calcs uses 5.67 ft, so the moments are about 1 % lower and the shears about 0.6 % lower than printed; the lintel weight and the span match. None on designs: the difference is the rounding of the published span.
• Height of the arching triangle in the NCMA TEK example. NCMA TEK 17-1D states that with arching action the lintel carries the wall within a triangle whose base is the effective span and whose height is half of it (2.83 ft in the example). Its worked example instead multiplies the wall weight by 3.5 ft, half the span plus the 8 in. of masonry required above the apex, giving 221 plf at midspan. ILX Calcs follows the text of the TEK: 179 plf at midspan, so the wall moment is 478 lb-ft against 598 lb-ft and the total moment 830 lb-ft against 955 lb-ft. ILX gives a wall load 19 % lower than the TEK example for arching; the engineer who prefers the example's rule can turn arching off for a full-height load or enter the extra wall weight as a load.
• Vertical seismic effect in the service deflection combination. FEMA P-1051 computes the mid-height deflection of the warehouse wall under dead load plus 0.7 times the seismic pressure. ASCE 7-22 2.4.5 also adds 0.7 times the vertical seismic effect, which is 0.14 times the short-period spectral acceleration times the dead load; with the example's 1.43 g the axial load becomes 1.2 times the dead load and the deflection 4.09 in. against FEMA's 3.85 in. Run without the vertical effect, ILX Calcs gives 3.87 in. ILX Calcs reports a larger service deflection when the vertical seismic effect is entered; both exceed the 2.35 in. limit.
• Flitch beam bolt value: one yield mode in the published example. The design example of DeStefano's flitch plate beam guide (STRUCTURE magazine, June 2007) takes the half-inch bolt value of 945 lb from the side member bearing mode of the NDS double shear equations only. With a steel plate as the middle member the NDS also requires the mode with a plastic hinge in the bolt and crushing of the wood plies, which gives 872 lb and governs. ILX Calcs reproduces the 945 lb value of the bearing mode and uses the least of all the yield modes. The bolt spacing is about 8 % closer and the number of end bolts about 8 % larger than in the example (20.3 in. instead of 21.9 in., 3.54 instead of 3.29 bolts before rounding up): conservative.
• Heel joint tension: truss joint in the HUD guide, rafter statics in the program. Example 7.3 of the HUD Residential Structural Design Guide (2000) finds the tension in the ceiling joist by resolving the rafter's bearing reaction along the rafter axis, as if the rafter were a truss member loaded only at its ends: 1,337 lb. A rafter carries its load along its length, so half of the load reaches the wall as shear in the rafter. Taking moments about the heel gives half of that force, 653 lb for this example, which is the program's value. The published printouts of another program and the nail counts of the IRC table agree with the moment balance. The bearing reaction itself, 652 lb, agrees. The program's tie force and nail count are about half of the example's (the guide itself says its 12 nails exceed conventional practice and suggests other methods). The IRC comparison is shown beside the count.
• Strength reduction factor of the 2022 edition in a column example. The TMS 2021 night school column example is written to TMS 402-16, which uses one strength reduction factor of 0.90 for all axial load and flexure. TMS 402-22 Table 9.1.4 sets the factor from the strain in the extreme tension bar: 0.65 when the section is compression controlled, 0.90 when it is tension controlled, and a straight line between. Pure axial load and the balanced point are compression controlled, so ILX Calcs uses 0.65 there. The nominal strengths of the example (axial strength 337.7 kips, balanced axial load 102.6 kips, balanced moment 82.6 kip-ft) match. ILX gives a lower design strength than the example, as the 2022 code requires: design axial strength 219.5 kips against 303.9 kips, and design moment at the balanced point 53.7 kip-ft against 74.36 kip-ft.
• Strength reduction factor of the 2022 edition in an out-of-plane wall example. FEMA P-1051 Section 13.1.5.2 is written to TMS 402-13, which uses one strength reduction factor of 0.90 for all axial load and flexure. TMS 402-22 Table 9.1.4 sets the factor from the strain in the tension bar. For the warehouse wall under 1.486 times the dead load that strain is 0.00478, just inside the transition region (the factor reaches 0.90 at 0.00507), so ILX Calcs uses 0.876. The nominal moment strength of the example (65.35 kip-in. per foot) matches, and under 0.614 times the dead load the factor stays 0.90 and the design strength matches. ILX gives a design moment strength 2.6 % lower than the example: 57.3 against 58.8 kip-in. per foot. With the iterative moment of 58.2 kip-in. per foot the wall passes in the example and is now 1.5 % over; with the moment magnifier it is over in both.
• Partially grouted wall factor changed in the 2022 code. The FEMA and TMS shear wall examples were written to the 2013 and 2016 codes, which multiply the shear strength of a partially grouted wall by 0.75. TMS 402-22 uses 0.70, so the program gives 6.7 percent less than these examples for the same wall. Shear strength of partially grouted walls is 6.7 percent lower than these older examples, which is conservative and follows the current code. Fully grouted walls are unchanged.
• Tension and shear interaction of two anchor examples. ACI SP-17(14) Anchorage Examples 10 and 11 add the tension and shear ratios using capacities they first round down to the nearest 100 lb (4,100 and 2,500 lb in Example 10, 3,900 and 2,500 lb in Example 11), and they print 1.05 and 1.08. The same sums with the capacities they calculated before rounding are about 1.03 and 1.06. ILX Calcs does not round the capacities, so it reports a sum about 2 % lower than the printed one. Every capacity in the two examples agrees within 1 %, and both designs pass in the example and in ILX Calcs.
• Reactions on the landing post and hanger of the Design Guide 34 stair. AISC Design Guide 34 Examples 10.1.3 and 10.1.4 add the 15.3 lb/ft beam self-weight into their factored line loads and print beam reactions of 5.90 and 1.80 kips, but Figures 10-5 and 10-6 leave it out of the dead load (0.0677 kip/ft is the landing load alone). Examples 10.1.5 and 10.1.6 then size the post and hanger from those figures: 5.82 and 1.71 kips, 3.98 and 1.15 kips in ASD. ILX Calcs keeps the self-weight and gives the printed beam reactions: 5.90 and 1.80 kips, 4.04 and 1.22 kips in ASD. The program's post and hanger loads are 1 to 6 % higher than the example, on the safe side. The strengths match.
• Velocity read from a chart in Design Guide 11 Example 6.3. AISC Design Guide 11 Example 6.3 reads the response from its Figure 6-15 to two digits and rounds it (290 mips for very slow walking). The program evaluates the Guide's Equation 6-3, the curve behind the figure. The program is about 4 % lower than the chart reading at very slow walking. It meets the same limit in the same way.
• Lateral moment on a sloped stair stringer. AISC Design Guide 34 Example 10.2.3 applies the seismic force per foot on plan and takes the lateral bending moment over the 14.7 ft span on plan: 0.540 kip-ft, or 0.284 kip-ft in ASD. Out of plane, the member spans its sloped length, 17.4 ft, and the total force is the same, so ILX Calcs multiplies the moment by the slope ratio 1.185 and gets 0.622 and 0.327 kip-ft. The interaction goes from 0.119 to 0.125 in LRFD, and from 0.123 to 0.127 in ASD. The program is about 19 % higher on this moment, on the safe side, and a little higher on the interaction. The example passes either way.
• Weld group centroid read from the Manual table in two Design Examples. Examples II.A-2B and II.A-29 interpolate the centroid distance in the x-bar row of the Manual table: 0.0269 and 0.0456. The centroid is a closed-form property of the lines, and it gives 0.0261 and 0.0449. The row is curved, so a straight line between tabulated k values sits above it. The centroid is 2 % to 3 % less than the example's, about 0.01 in. here. The coefficient C and the strength of both examples still match within tolerance.
• Manual Table 8-11a at 75 degrees, small eccentricity. On the 75 degree page of Table 8-11a, the cells at a = 0.10 and 0.15 from k = 0.8 up are the same as the concentric row of the page, while the instantaneous center method gives 1.1 % to 1.6 % more. Other pages of the tables do go above their concentric row, so this is not a general cap, and the Manual does not explain it. Eleven cells. The program is up to 1.6 % above the table for those cells. The program solves the method as the Manual describes it, and shows the table value beside its own.
• Manual Table 8-10 at 0 degrees, k = 2.0, a = 0.10. The table prints 7.10. The instantaneous center method has one solution at this cell, 7.19. The concentric row of the page is 7.15, so the concentric strength does not explain the printed value either. The program is 1.3 % above the table for this cell and shows the table value beside its own.
• Manual Table 8-4 at 0 degrees, k = 2.0, three cells. At a = 0.70, 2.4 and 2.6 the table prints 2.45, 1.24 and 1.17, and the method gives 2.43, 1.23 and 1.16. The Manual builds its tables with a convergence criterion of 0.5 %, and these cells are just past 1 %. Both machine reads of the page agree on the printed values. The program is 1.0 % to 1.1 % below the table for those cells, on the safe side.
• Pryout area of a stud group. ACI SP-17(14) Anchorage Example 14 takes the pryout strength of a group of eight studs from the breakout area of its top row alone. ACI MNL-17(21) Anchorage Example 17 (Vol. 2 pp. 400 and 403), the same plate, does the same (1,233 square inches, 121,482 lb), and says itself that all studs welded to the plate resist the shear and that assigning it to the top row is conservative. ILX Calcs uses the area of the whole group, as Chapter 17 reads for a welded group. Its pryout strength is higher than printed. Pryout does not govern this example.
• An older strength reduction factor in a deep beam limit. ACI SP-17(14) Strut-and-Tie Example 1 prints the limit on the shear of a deep beam with a factor of 0.85, the value of older codes. ACI 318-14 and 318-19 have 0.75 for shear. ACI MNL-17(21) Strut-and-tie Example 1 (Vol. 2 p. 210) still prints 0.85 (1,064 kips). ILX Calcs uses 0.75, so its limit is about 12 % lower than printed. The example's shear is far under either limit.
• Strut factor without distributed steel. The example is to ACI 318-14, where an interior strut without distributed steel takes a factor of 0.6. ACI 318-19 Table 23.4.3(a) lowered this to 0.4. ACI MNL-17(21) Strut-and-tie Examples 1 to 3 (Vol. 2 pp. 204, 214 and 228) list 0.4 for an interior strut without the minimum distributed steel, as Table 23.4.3(a) does. ILX Calcs follows 318-19, so this strut's strength is one third lower than the older figure. With the distributed steel both editions give 0.75 and the values agree.
• Depth of the node used for a tie's anchorage. StructurePoint DE-STM measures the extended nodal zone from a tie node 13.4 in. deep, worked out from a stress. Here the node depth is the 10 in. the engineer entered, as the same example assumes at the start. The extended zone is 8.0 in. here against 10.7 in. printed, which is on the safe side for anchorage. The forces do not change.
• Pullout factor of a cast-in stud. ACI SP-17(14) Anchorage Example 14 uses a strength reduction factor of 0.75 for pullout, the value ACI 318-14 gives with supplementary reinforcement. ACI 318-19 Table 17.5.3(c) has 0.70 for cast-in anchors. ACI MNL-17(21) Anchorage Example 17 (Vol. 2 pp. 399 and 403) still takes 0.75 for pullout and pryout because supplementary reinforcement is present. ACI 318-19 Table 17.5.3(c) gives pullout and pryout of cast-in anchors 0.70 with no case for supplementary reinforcement. ILX Calcs follows 318-19: its design pullout strength is about 7 % lower than printed. Pullout does not govern this example.
• Load-bearing length of a stud in shear. ACI SP-17(14) Anchorage Example 14 takes the load-bearing length of the stud as its full embedment when it finds the basic shear breakout strength. The code limits that length to 8 stud diameters, 5 in. for this stud. ACI MNL-17(21) Anchorage Example 17 (Vol. 2 p. 402), the 2021 version of this example, applies the limit (5 in.) as ILX Calcs does; there the 9 root f'c times ca1 to the 1.5 expression governs, 99,386 lb. ILX Calcs applies the limit, so its shear breakout strength is about 6 % lower than printed and the interaction of tension and shear about 4 % higher. The design is still adequate. Part of the difference is not the length limit: for welded studs ILX Calcs uses the coefficient 7 of 17.7.2.2.1 where 17.7.2.2.2 permits 8 under its conditions (see MNL17-A17-VB), which is conservative.
• Lever arm of the masonry in a retaining wall example. CMHA TEK 15-07B puts the masonry stem's weight 2.67 ft from the toe, the footing's centre. Its own drawing gives 1.67 ft of toe plus half of a 0.97 ft wall, 2.15 ft. It then adds a resisting moment of 16,194 ft-lb/ft but divides 14,670 by the overturning moment for its factor of safety. ILX Calcs takes the geometry: resisting moment about 15,620 ft-lb/ft, factor of safety 2.62 where the note prints 2.4, resultant 2.06 ft from the toe where it prints 2.18 ft, toe pressure 1,481 psf where it prints 1,356 psf, heel pressure 280 psf where it prints 404 psf. The design conclusion, resultant in the middle third and pressure below 2,000 psf, holds either way.
• The key's own weight in a retaining wall example. CMHA TEK 15-07B turns the average bearing pressure into a soil depth to find the pressure on the key, with the wall's weight before the key was added. ILX Calcs includes the key's weight, about 200 lb per foot, so its pressures are about 4 % higher: 1,148 and 1,347 psf where the note prints 1,100 and 1,300 psf. This option is off by default.
• Second-order moment in a Masonry Designers' Guide example. The Masonry Designers' Guide 2022, Example 17.2-5, writes the second-order moment of a cantilever correctly, then drops the 5 from the denominator when it substitutes numbers, and prints 22,710 lb-in. per foot. The Guide's own equation with its own numbers gives 21,464 lb-in. per foot, about 5 % lower, and ILX Calcs uses the equation. The example's GFRP bars are not part of this calculation; only the equation transfers.
• Design Example F.8B, slender flange of a square HSS. The Example removes the ineffective width from both flanges, which it says is a simpler and conservative way to get the effective section modulus. The Specification's own method removes it from the compression flange only and lets the neutral axis move, and the program does that. The program is 1.9 % above the Example, 46.3 against 45.4 kip-ft LRFD, 30.8 against 30.2 kip-ft ASD. The effective width itself agrees.
• Design Example F.11B, leg local buckling of an angle restrained at midspan. The Example reuses the leg local buckling strength of Example F.11A, which has the 0.80 reduction for an angle without restraint, and says this is conservative because the angle here is restrained at midspan. The Specification applies the reduction only without restraint, and the program follows it. Lateral-torsional buckling then governs, and that value agrees with the Example's 5.53 kip-ft. The program gives 4.97 kip-ft LRFD against the Example's 3.98, and 3.31 against 2.65 ASD. The Example itself states its value is on the safe side.
• Distortional half-wavelength of a Z-section. The MBMA Guide reads the half-wavelength of the Z-sections from a table in the AISI Design Manual: 21.7 and 25.4 in. The Specification's equation with its table of mid-line flange properties, which leaves out the corner radii, gives 22.1 and 25.8 in. here, about 2 percent longer. On the C-sections of the same Guide the same equation lands on the printed values, so the difference is in how the Manual treats the sloped lip, which the paid Manual would show. None that matters on strength: the distortional buckling stress at this length lands within 0.3 percent of the Guide's 51.1 and 32.5 ksi.
• Web geometric stiffness of a Z-section. The web's geometric rotational stiffness depends on the half-wavelength above, so it differs from the printed 0.00259 and 0.00132 by about 2 to 4 percent. It is a small part of the denominator: the buckling stress still lands on the printed value.
• Inflection point in the MBMA Guide's four span example. The Guide's moment diagram puts the inflection points about 0.04 ft nearer the lap ends than this analysis of the same line does, within the 0.05 ft a printed diagram can hide. Every printed moment, shear and reaction agrees within 1 percent. The lateral-torsional buckling stress goes with the inverse square of this length and with 1.67 where the equation gives 5/3, so it reads up to 3 percent lower. None: both buckling stresses are far over the limit where the flexural stress equals the yield stress.
• Torsional stress of a C-section in the MBMA Guide. MBMA Example 3.3.2.2 computes the torsional buckling stress with the polar radius of gyration to the first power, 452 ksi. The Specification squares it, which gives about 116 ksi, so the elastic stress here is 262 ksi against the printed 542 ksi. The example also prints a polar radius of 5.26 in. that it does not use. None on this example's strength: both are well over the limit where the flexural stress equals the yield stress. On longer unbraced lengths the printed form would overstate the strength; this calculation follows the Specification.
• LRFD wind factor in the MBMA Guide. MBMA Example 3.3.2.2 takes 0.9 dead plus 1.6 wind for LRFD uplift. It names ASCE 7-16, whose wind load factor is 1.0, and the Guide's own ASD examples use 0.6 wind, which is the same basis as 1.0. This calculation uses ASCE 7-22, 0.9 dead plus 1.0 wind. The example's uplift moments are 4.83 and 2.10 kip-ft; here they are 2.76 and 1.20 kip-ft on the wind as printed. Entered as 1.6 times the printed wind, the calculation lands on the printed moments, which a separate row shows. The strength side agrees.
• Slenderness rounded in a single-angle example. AISC Design Example E.14A rounds the modified slenderness of the L5x3x1/2 up to 127 before finding the buckling stress. Unrounded it is 126.6. ILX Calcs does not round, so its design strength is 52.8 kips where the Example prints 52.3 kips, about 1.05 % higher. The allowable strength agrees within 1 %.
• Deck web crippling on another maker's web geometry. The Vulcraft catalog prints allowable reactions for its 1.5PLB22 deck but not the bend radius or web angle behind them. This comparison uses those of Verco's PLB-36, 22 gage, a similar deck of the same group. ILX Calcs gives 911.8 and 1,344 lb per foot where the catalog prints 897 and 1,325, about 1.5 % higher, on the unsafe side of the printed values. The ratio between bearing lengths matches the catalog. When your manufacturer prints its reactions, enter those values instead of the geometry.
• Deck web shear against a catalog value. The Vulcraft catalog prints an allowable web shear of 2,825 lb per foot for its 1.5PLB22 deck, without the web's geometry or how the value is reached. This comparison uses Verco's web geometry and the S100-16 safety factor of 1.60. ILX Calcs gives 2,651 lb per foot, about 6 % lower, on the safe side. The same equations reproduce the nominal shear Verco's IAPMO report prints for four gages.
• Joint coefficient of a special moment frame in the 2021 handbook. ACI MNL-17(21) Columns Example 4 (p. 426) checks a special moment frame joint under Table 18.8.4.3 but takes the coefficient 20, the value of Table 15.4.2.3 for a continuous column and beam without confining transverse beams. Table 18.8.4.3 gives 15 for that joint. The same line prints 0.85 times 814 as 610 kips; the product is 692. ILX Calcs uses 15: 611 kips nominal and 519 kips design strength, 25 percent below the printed nominal value, on the conservative side. The joint still passes (424 kips).
• One-way shear of a footing with the minimum steel ratio. ACI MNL-17(21) Foundation Example 1 (p. 480) sizes the footing for one-way shear with a steel ratio of 0.0018, the minimum flexural steel, which gives a design strength of 208 kips, and keeps that check after choosing 13 No. 8 bars each way. ILX Calcs uses the bars provided, a ratio of about 0.0023 at the upper layer. ILX Calcs' strength is about 9 percent higher than the printed estimate, as the steel provided gives. The factored shear matches and the footing passes either way.
• Factored pressure on a width other than the footing's. ACI MNL-17(21) Foundation Example 2 (p. 490) divides the factored load of 50 kips per foot by 9.5 ft to print 5.26 ksf, then uses that pressure on the 10 ft footing it adopts, for the moment of 53.3 kip-ft per foot. On 10 ft the pressure is 5.0 ksf. Its first shear equation (p. 491) gives the printed d of 23.2 in. only with 5.0 ksf, and its second does not give the printed 18.1 in. with either pressure (about 20.6 in. with 5.0 ksf). ILX Calcs gives 5.0 ksf and 50.6 kip-ft per foot, 5 percent below the printed values, as the adopted width gives. With the thickness and bars the example adopts (24 in., No. 8 at 12 in., d = 20.5 in.), ILX Calcs finds the one-way shear about 1 percent over the strength (13.96 against 13.77 kips per foot), which the handbook does not check.
• Minimum steel on an earlier trial thickness. ACI MNL-17(21) Foundation Example 2 (p. 492) takes the minimum flexural steel as 0.0018 times 12 in. times 20 in., and the strain check with d = 16.5 in., both from a 20 in. thickness, while the footing it adopts and details is 24 in. thick with d = 20.5 in. ILX Calcs uses the 24 in. thickness: 0.52 square inches per foot instead of 0.43. The No. 8 bars at 12 in. (0.79) satisfy both.
• Heel loads. ACI MNL-17(21) Retaining Walls Examples 2 to 6 design the heel for the soil weight times 1.6 and the heel weight times 1.2 and ignore the soil pressure pushing up under the heel. ILX Calcs uses the base pressure from the factored loads of each ASCE 7 combination and treats the soil over the heel as dead load. ILX Calcs' heel moment and shear are lower than the handbook's. Both are statics on a stated load model; the handbook's is the more conservative.
• Toe base pressure. ACI MNL-17(21) Retaining Walls Examples 2 and 4 multiply the service base pressure by 1.6 for the toe. ILX Calcs works out the base pressure from the factored loads of each ASCE 7 combination; 0.9D + 1.6H governs. ILX Calcs' toe moment and shear are about 5 to 10 percent lower.
• Load combination for the basement wall moment. ACI MNL-17(21) Retaining Walls Example 1 multiplies the whole service span moment by 1.6, including the end moment from the slab dead and live load, which reduces the span moment. ILX Calcs checks the ASCE 7 combinations, and 0.9D + 1.6H with no live load reduces it less. ILX Calcs' moment is higher, about 4.0 against 3.76 kip-ft per foot (conservative).
• Axial load in out-of-plane shear. ACI MNL-17(21) Retaining Walls Example 1 takes the axial load as zero in the shear strength. ILX Calcs adds Nu/(6Ag) for the factored axial load at the section, as Table 22.5.5.1(c) permits. ILX Calcs' Vc is about 5 percent higher.
• Misprint in the revised summary. ACI MNL-17(21) Retaining Walls Example 2 prints a stem shear strength of 17,500 lb in the summary of the revised design. The stem and its bars did not change, and the handbook's own calculation gives 9.90 kips. None; ILX Calcs matches 9.90 kips.
• Earth pressure coefficient for a sloped backfill. ACI MNL-17(21) Retaining Walls Example 3 uses the level-ground Rankine coefficient, 0.282, for a 10 degree backfill slope. Rankine's coefficient for a sloped backfill is 0.294. ILX Calcs' lateral force and overturning moment are about 4 percent higher and its factors of safety lower; at 0.294 the handbook's wall does not reach a factor of safety of 1.5 against sliding.
• Stem pressure height with a sloped backfill. ACI MNL-17(21) Retaining Walls Example 3 applies its pressure over 14.84 ft, the height of the plane through the heel less the footing, to a 14 ft stem. ILX Calcs applies the Rankine pressure measured from the top of the stem. ILX Calcs' stem moment is about 25.5 against 29.0 kip-ft per foot; the handbook's is a conservative simplification.
• Tension strain in Beam Example 1 Table 1.2. ACI MNL-17(21) Beam Example 1 lists net tensile strains for the positive-moment sections that do not follow from the stress block depths printed in the same table. For five No. 7 bars, a = 0.35 in. and c = a/0.8 = 0.44 in. give 0.003(27.5 - 0.44)/0.44 = 0.184, where the table prints 0.166; for four No. 7 bars the strain is 0.230 against 0.208. ILX Calcs computes the strain from the neutral axis depth. ILX Calcs' strains are about 10 percent higher. Both are far above 0.005, so the sections are tension-controlled either way.
• Crack-control bar spacing with the cover rounded. ACI MNL-17(21) Beam Example 1 takes the clear cover to the No. 7 bars as 2 in. in the Table 24.3.2 spacing limit. With 1.5 in. cover and No. 3 stirrups the cover is 1.875 in., which gives 15(40,000/40,000) - 2.5(1.875) = 10.3 in. ILX Calcs allows 10.3 in. against the handbook's 10 in. The bars provided are much closer than either.
• Section size limit for shear in Beam Example 4. ACI MNL-17(21) Beam Example 4 writes the limit of Eq. 22.5.1.2 as 0.75(70.3 kips + 8 times root f'c bw d) but prints 211 kips, which is 0.75 times the second term alone. With Vc included the limit is 0.75(70.3 + 281.1) = 263.6 kips. ILX Calcs' limit is 263.6 kips. The factored shear of 47 kips is far below either value.
• Minimum longitudinal torsion steel uses the required At/s. In 9.6.4.3(a), ACI MNL-17(21) Beam Example 4 uses the At/s of the stirrups provided (two No. 4 legs at 10 in., 0.02 in.2/in.). ILX Calcs uses the At/s required for torsion (0.0071 in.2/in.), so 9.6.4.3(a) gives 3.55 in.2 and the lesser value, (b), is 3.52 in.2. The handbook gets 2.49 in.2. ILX Calcs asks for about 1 in.2 more longitudinal torsion steel in this example (conservative).
• Minimum longitudinal torsion steel in Beam Example 9. ACI MNL-17(21) Beam Example 9 copies the 9.6.4.3 calculation from Example 8, including Example 8's At/s of 0.0324 in.2/in. With this example's reduced torsion, At/s is 0.0199 in.2/in., and 9.6.4.3(a) gives 2.26 - 0.0199 x 66 = 0.95 in.2, not 0.12 in.2. ILX Calcs' minimum is 0.95 in.2 against the handbook's 0.12 in.2. The 1.32 in.2 required by Eq. 22.7.6.1b still governs, so the design does not change.
• Effective moment of inertia for dead plus live load in Deflection Example 2. ACI MNL-17(21) Deflection Example 2 says it takes Ie for dead plus live load from Example 1 (11,100 in.4) but divides by 11,400 in.4, the dead-load value. With 11,100 in.4 its own numbers give a total deflection of 1.28 in. and a live load deflection of 0.43 in. instead of 0.4 in. ILX Calcs computes Ie for each load level by Table 24.2.3.5. ILX Calcs' live load deflection is 0.42 in. against the handbook's 0.4 in. (conservative).
• Negative-moment cracking moment of a T-section read from a chart. ACI MNL-17(21) Deflection Example 7 reads the T-section factor Kcrt = 2.3 for negative moment from Design Aid 13.3.1. Calculated directly, fr Ig/yt of the section gives Kcrt = 2.39 and Mcr = 402 ft-kip, against the handbook's 387 ft-kip. The positive-moment value agrees (229 ft-kip). ILX Calcs' negative-moment Mcr is about 4 percent higher; the difference is the chart reading.
• Cm rounded before the magnifier. ACI MNL-17(21) Columns Example 1 (p. 401) rounds Cm = 0.6 - 0.4(1962/2634) = 0.302 to 0.30 and then computes δ = 1.07 and Mc = 2,820 kip-in. (p. 402). With 0.302 the magnifier is 1.08 and Mc is 2,849 kip-in. ILX Calcs' δ and Mc are about 1 percent higher than printed, on the conservative side. Pc (1,460 kips) and (EI)eff agree.
• Nominal moments from the handbook's spreadsheet at the lower axial load. ACI MNL-17(21) Columns Examples 3 (p. 414) and 4 (p. 420) print Mn from the interaction diagram spreadsheet. At the higher axial loads (848 and 872 kips) strain compatibility of the stated bars agrees within 1 percent. At the lower loads the printed 7,994 and 8,380 kip-in. are not reproduced: a hand calculation at Pn = Pu gives 7,765 and 7,842 kip-in., as ILX Calcs does. ILX Calcs' nominal moments at the lower loads are 2.9 and 6.9 percent below the printed values (conservative).
• Distributed wall bars placed from s/2 at each end. The ACI MNL-17(21) shear wall spreadsheet puts the first pair of bars 3 in. and the second 12 in. from each end, then every 12 in. (29 positions in 28 ft). ILX Calcs spaces the distributed bars at s, starting s/2 from each end (28 positions). Design flexural strength at Pu = 1,015 kips is 1.9 percent lower in Example 1 (24,130 against 24,600 kip-ft) and 2.9 percent lower in Example 2 (39,050 against 40,200 kip-ft). Concentrated end bars can be entered to model bars near the ends.
• Minimum vertical wall steel not taken below 0.0025. ACI MNL-17(21) Shear Wall Example 1 (p. 448) reads 11.6.2(a) literally: the vertical ratio need not exceed the horizontal ratio required for strength, which is zero there, so it sets the minimum to zero. ILX Calcs does not go below 0.0025, because the horizontal ratio itself must be at least 0.0025 by 11.6.2(b). The example's Eq. 11.6.2 line also uses hw/lw = 2 where the wall has 3.3; the result would be 0.0025 either way. ILX Calcs asks for 0.36 in.2 per foot of vertical steel where the example asks for none. The No. 5 at 12 in. each face provided passes either way.
• Shear strength reduction factor of a wall designed by the displacement method. ACI MNL-17(21) Shear Wall Example 2 (p. 457) uses φ = 0.60 for shear because Vn is less than the shear that develops the nominal moment (21.2.4.1). ACI 318-19 18.10.4.6 (p. 323) states that 21.2.4.1 does not apply to walls or wall piers designed according to 18.10.6.2, as this one is; R18.10.4.6 explains that such walls are controlled by flexural yielding and their shear is already amplified. ILX Calcs uses φ = 0.75 for them, and 0.60 under 21.2.4.1 for other special walls. Design shear strength is 1,537 kips against the printed 1,227 kips. Both exceed Ve = 1,107 kips. Vn itself agrees (2,049 against 2,045 kips).
• Neutral axis depth for the boundary element check. ACI MNL-17(21) Shear Wall Example 2 (p. 458) takes c = 67.9 in. from its software, with its own bar layout (bars 3 in. from each end). With No. 8 at 12 in. each face placed from s/2, ILX Calcs computes c = 65.3 in. at Pu = 1,015 kips. The required width by the square-root expression is 23.4 in. against 23.9 in. Special boundary elements are required either way, and the 12 in. wall fails both alternatives in both.
• Drift capacity reported at its 0.015 floor. Eq. 18.10.6.2b need not be taken below 0.015. ACI MNL-17(21) Shear Wall Example 2 (p. 459) prints the raw value 0.0035 for b = 12 in.; ILX Calcs reports 0.015. Both are below 1.5 δu/hwcs = 0.0163, so the wall fails at b = 12 in. either way, as the example concludes.
• Shear fraction of the transferred moment at an edge column. ACI MNL-17(21) Two-way Slab Example 3 (p. 136) takes γv = 0.4 at the edge column. With b1 = 28.5 in. and b2 = 33 in., Eq. 8.4.2.2.2 gives γf = 0.617 and γv = 0.383. The moment stress is 75.9 psi against 79 psi, and vu is 146 psi against 149 psi, 2 percent lower. Both are well below φvc = 212 psi.
• The αs term of the third vc expression. ACI MNL-17(21) Two-way Slab Example 3 (p. 137) uses αs d/bo = 2.73 at the edge column and 2.5 at the interior column. With αs = 30 and 40, d = 9 in. and bo = 90 and 132 in., the terms are 3.0 and 2.73; the printed values look swapped. The third expression is 354 and 334 psi against the printed 334 and 318 psi. It does not govern: 4λ√f'c = 283 psi governs in both.
• Development length rounded up. ACI MNL-17(21) One-way Slab Example 1 (p. 55) prints ℓd = 19 in. for a No. 5 bar with (cb + Ktr)/db = 1.7; the equation gives 18.7 in. The lap of 1.3 x 19 = 24.7 in. (p. 56) carries the rounding. ILX Calcs gives 18.7 in. and a 24.3 in. Class B lap, 1.5 percent below the printed values.
• Simplified development length with the other-cases coefficient. ACI MNL-17(21) Columns Example 5 (p. 429) states that the No. 8 bars have clear spacing of at least 2db and clear cover of at least db, which is the first row of Table 25.4.2.3. It then uses the other-cases expression 3fy/(40λ√f'c) db, giving 63.6 in. The first row gives fy/(20λ√f'c) db = 42.4 in. ILX Calcs gives 42.4 in. The printed 63.6 in. is conservative, and its 1.25ℓd check against ℓu/2 passes either way.
• Hook length of a No. 6 bar computed with the No. 5 diameter. ACI MNL-17(21) Shear Wall Example 2 (p. 463) checks the hook of the No. 6 horizontal bars with db = 0.625 in., the No. 5 diameter, and gets 7.1 in. With db = 0.75 in. the same factors give 9.4 in. ILX Calcs' hook length is 31 percent longer than printed, on the safe side; the 26.5 in. available still suffices.
• Screw anchor steel strength in the summary. ACI MNL-17(21) Anchorage Example 4 (Vol. 2 p. 286) lists a design steel strength of 12,700 lb for the 3/4 in. screw anchor in its summary table. That is the value of the 5/8 in. expansion anchor of Example 3. The book's Table E.2 (p. 487) gives the 3/4 in. screw anchor an effective area of 0.403 in.2 and futa of 75,000 psi, and the example takes φ = 0.65 for brittle steel, so φNsa = 0.65 × 0.403 × 75,000 = 19,646 lb. ILX Calcs gives 19,646 lb from the table data. Steel does not govern: concrete breakout at 7,235 lb controls in both, and that value matches.
• Bond stress of the 1/2 in. adhesive anchor. ACI MNL-17(21) Anchorage Example 5, Part B (Vol. 2 p. 296), says it takes τcr from Table E.3 and prints 1,120 psi, giving Nba = 6,157 lb, φNa = 2,770 lb and a sustained strength of 1,500 lb. Table E.3 (p. 488) gives 1,030 psi in cracked concrete and 2,240 psi in uncracked concrete for the 1/2 in. anchor; 1,120 psi is not in it. The example's own summary table prints φNa = 2,500 lb, which follows from 1,030 psi (2,548 lb). ILX Calcs uses the table value of 1,030 psi and gives Nba = 5,663 lb, φNa = 2,548 lb and a sustained strength of 1,401 lb, about 8 percent below the printed values, on the safe side. The anchor still passes the 880 lb demand.
• Splitting factor of an adhesive anchor in cracked concrete. ACI MNL-17(21) Anchorage Examples 9 and 14 (Vol. 2 pp. 325 and 373) apply ψcp,Na below 1.0 to an adhesive anchor in concrete taken as cracked. ACI 318-19 17.6.5.5.1 applies this factor only to anchors designed for uncracked concrete, and 17.6.5.5.2 makes it 1.0 in all other cases. In Example 9 the printed Na of 5,216 lb is in fact computed without the factor; in Example 14 it lowers Na to 5,277 lb. ILX Calcs takes ψcp,Na = 1.0 in cracked concrete. It matches Example 9's Na and gives 5,997 lb for Example 14 (φNa 3.90 against 3.43 kips, interaction 1.06 against 1.15), following the code.
• Strength reduction factor for pryout of an adhesive anchor. ACI MNL-17(21) Anchorage Example 9 (Vol. 2 p. 325) takes φ = 0.65 for concrete pryout, the factor of the adhesive's Category 1, and prints φVcp = 6,780 lb. ACI 318-19 Table 17.5.3(c) gives 0.70 for pryout of cast-in and post-installed anchors alike; the category factors in that table apply to pullout only. The book's Examples 7 and 8 use 0.70 for the same check. ILX Calcs gives 0.70 × 10,432 lb = 7,302 lb, about 8 percent above the printed 6,780 lb, as the code requires. Shear breakout at 1,495 lb governs the anchor in both.
• Tension and shear interaction of a cast-in bolt at a beam end. ACI MNL-17(21) Anchorage Example 10 (Vol. 2 p. 335) adds 1,935 lb over 6,300 lb and 1,440 lb over 2,500 lb, capacities it first rounds down from 6,363 and 2,573 lb, and prints 0.89. Those two ratios add to 0.88; with the unrounded capacities the sum is 0.87. ILX Calcs does not round the capacities and gives 0.87, about 2 percent below the printed value. Every capacity in the example agrees within 1 percent, and the anchor passes in both.
• Tension and shear interaction of a hooked bolt. ACI MNL-17(21) Anchorage Example 11 (Vol. 2 p. 345) finds that pullout governs tension at φNpn = 3,308 lb (3,300 lb in its summary), then divides Nua = 1,935 lb by 4,400 lb in the interaction and prints 1.02. No 4,400 lb strength appears in the example. With the governing 3,300 and 2,500 lb the sum is 1.16; with the unrounded strengths it is 1.15. ILX Calcs uses the governing tension strength and gives 1.15, higher than the printed 1.02 and on the safe side. The anchor still passes the 1.2 limit.
• Shear breakout of the screw anchor multiplied by the wrong value. ACI MNL-17(21) Anchorage Example 13 (Vol. 2 p. 364) computes Vcb = 3,675 lb and then prints φVcb = 0.7 times 3,515 lb = 2,460 lb. With its own Vcb, φVcb is 2,570 lb, as in Examples 12 and 14 on the same beam. Its interaction (p. 365) adds 1,935/4,100 and 1,440/2,400, which is 1.07, and prints 1.05. ILX Calcs gives φVcb = 2.57 kips and an interaction of 1.02. The publication is the more conservative by about 4 percent on breakout; the anchor passes either way.
• Bond strength used in the adhesive anchor pryout. ACI MNL-17(21) Anchorage Example 14 (Vol. 2 p. 376) takes Na = 5,692 lb in the pryout check. Its bond step (p. 373) gives Na = 5,277 lb with ψcp,Na = 0.88, and ACI 318-19 gives 5,997 lb (ψcp,Na = 1.0 in cracked concrete). The value 5,692 lb follows from neither. ILX Calcs gives φVcp = 0.70 times 2 times 5,997 lb = 8.40 kips against the printed 7.97 kips, 5 percent higher, following the code. Pryout does not govern this anchor.
• Basic shear breakout strength of studs welded to a plate. ACI MNL-17(21) Anchorage Example 17 (Vol. 2 p. 402) has 5/8 in. studs welded to a 1-1/2 in. plate. It takes Vb as the lesser of 9 λa √f'c ca1^1.5 and the expression of 17.7.2.2.2 with the coefficient 8, which ACI 318-19 permits for studs continuously welded to an attachment at least da/2 and 3/8 in. thick under further conditions; the 9 √f'c expression governs at 99,386 lb. ILX Calcs uses the general expression of 17.7.2.2.1 with the coefficient 7 for welded studs as well, which governs at about 92,600 lb. ILX Calcs gives a basic and group shear breakout strength about 7 percent lower than printed (Vcbg about 46,100 lb against 49,253 lb), and a tension and shear interaction about 4 percent higher. This is on the safe side; the design is still adequate.
• Tension φ without the credit for supplementary reinforcement. ACI MNL-17(21) Anchorage Examples 20 and 22 state that supplementary reinforcement is detailed, yet take φ for adhesive bond (and in Example 20 also for concrete breakout) from the product data table, 0.65 for Category 1 and 0.55 for Category 2. Those are the ACI 318-19 Table 17.5.3(b) values without supplementary reinforcement. With it, the table gives 0.75 and 0.65. Example 16 uses 0.75 for breakout in the same situation, and Example 22 uses 0.65 (Category 2) for its breakout. ILX Calcs applies Table 17.5.3(b) as stated: Example 20 gives φNcbg = 22.07 and φNag = 16.57 kips against 19.14 and 14.36, and Example 22 gives φNag = 23.8 against 20.3 kips. The publication is more conservative; the engineer can enter no supplementary reinforcement to get its values.
• Pryout area of a base plate rod group. ACI MNL-17(21) Anchorage Example 21 (Vol. 2 p. 462) takes the pryout strength of four rods from the breakout area of one row of two (512 square inches, Ncpg = 39,628 lb, Vcpg = 79,256 lb) and takes φ as 0.75. ACI 318-19 17.7.3 takes Ncpg as the breakout strength of the anchor group, and Table 17.5.3(c) gives φ = 0.70 for cast-in anchors in pryout. ILX Calcs uses the whole group (1,024 square inches, Vcpg = 158.5 kips, φVcpg = 110.9 kips), higher than printed. Pryout does not govern this example.
• Pryout of the base plate group from the back row only. ACI MNL-17(21) Anchorage Example 22 (Vol. 2 p. 478) computes pryout from the breakout of the back two anchors only (ANc = 392 square inches, Ncbg = 19,900 lb) with φ = 0.75. It also uses 4.5 cNa squared for ANao in that step. ACI 318-19 17.7.3 takes Ncpg of the group, here the four anchors, the lesser of breakout (39.8 kips) and bond (36.7 kips), and Table 17.5.3(c) gives φ = 0.70 for pryout. ILX Calcs gives φVcpg = 0.70 times 2 times 36.7 = 51.3 kips against the printed 29.85 kips. This is higher because the whole group is used, as in the code; the same choice is recorded for the embed plate (SP17-E14-PRYOUT).
• Groundwater factor rounded in the published example. The FHWA shallow foundations circular works the bearing capacity of an interior pier and rounds the groundwater correction factor of the unit weight term to 0.9. Its own equation gives 0.878 for the 6 meter width used. ILX Calcs keeps the equation's value, so the unit weight term is about 2 percent lower than printed (1,487 against 1,524 kPa). The surcharge term and every factor match.
• Rigid gust factor in the commentary table does not follow from its own inputs. The ASCE 7-22 commentary table of gust factors lists a turbulence intensity of 0.201 and a background response squared of 0.616 for its 600 foot building, and prints a calculated rigid gust factor of 0.860. The standard's equation with those two values gives 0.818. Every other value in the table, including the flexible factor of 1.162, is reproduced. ILX Calcs gives 0.818, the equation's value, about 5 percent below the printed number. The flexible factor, which this building must use, matches.
• Commentary acceleration uses the resonant response of the design wind speed. The commentary example of along-wind acceleration works the acceleration at a 76 mph serviceability wind but lists the resonant response factor 1.123, which is the value at the 115 mph design wind. The resonant response depends on the wind speed, and at 76 mph the standard's equation gives about 0.74. ILX Calcs evaluates the resonant response at the serviceability speed, so its acceleration is about 0.126 instead of 0.176 feet per second squared, and its peak about 0.48 instead of 0.668. The displacement and the peak factor match the example.