Ledge and inverted-tee beam
The ledge of a spandrel (L-beam) or an inverted-tee beam carrying repeated bearings (double-tee stems, joists): the punching shear of the ledge, its flexure and direct tension, the hanger reinforcement that lifts the load into the web, the bearing, and the shear and torsion of the beam. The ledge rules follow the PCI Design Handbook ledge method, which is not on disk: those steps are written from knowledge and marked "to confirm against the code text". ACI 318-19 (on disk) gives the bearing, the shear and the torsion (22.5, 22.7, 22.8).
Inputs of the ledge #
- Beam and ledge: spandrel or inverted tee (two ledges loaded alike), web width and depth, ledge projection and depth, cover, span, other dead load on the beam.
- Bearings: spacing along the beam, bearing width (along the beam) and length (across the ledge), the distance av from the web face to the load, the distance de from the beam end to the first load, the loads per bearing by load type, and the horizontal force as a fraction of Vu (0.2 usual).
- Reinforcement: ledge bars and spacing, hanger bars and spacing (the legs on the ledge side), closed web stirrups and the longitudinal torsion bars provided.
Auto-design varies the ledge depth and the ledge bar, hanger and stirrup spacings.
Checks performed #
| Check | Basis |
|---|---|
| Ledge punching, interior and near the end | Vn = 3λ√f'c hl (2 le + w), w = least of bt + hl and s; at the end half of it plus the end distance (PCI, to confirm) |
| Ledge flexure and direct tension | As = (Vu av + Nu (hl − d))/(φ fy d) + Nu/(φ fy) within bt + 5av, not more than s (PCI, to confirm; ACI 318-19 16.5 analogy) |
| Hangers | Ash = Vu/(φ fy) within bt + 3av, not more than s (PCI, to confirm) |
| Bearing | ACI 318-19 22.8.3.2, φ = 0.65 |
| Beam shear | ACI 318-19 22.5 at the support with the bearing loads as a line load |
| Spandrel torsion | Tu = (Vu/s) e L/2 at the support, ACI 318-19 22.7 (section size, stirrups, Al, spacing) |
The drawing is a section at a bearing with the ledge bars and hangers.
Limitations #
- The PCI ledge equations, effective widths and end rules are from knowledge (to confirm against the code text).
- Loads of one size at one spacing; the strut-and-tie alternative, the beam's flexure, dapped ends and connections are not covered. The torsion is uniformized over the span.
Verification examples #
Verification status: 8 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 8 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: written without the code document on hand, and confirmed only in part through published examples.
No published ledge example is on disk. Hand calculations (closed form) check Vu, the punching strength, the ledge and hanger steel, the bearing and the spandrel torsion, and the spacing limit on the punching width.