Punching shear

Two-way shear at a column, concentrated load or reaction area to ACI 318-19 22.6 and 8.4.4: the critical section at d/2, moment transfer by eccentric shear, the concrete strength with its size effect, stirrups or headed shear studs, and the section outside the shear reinforcement. ACI 318 has one method for this check, strength design, so the type has no LRFD / ASD switch. Enter factored values; combine the loads by ASCE 7-22 2.3 first. Use it to check a slab analysed elsewhere, or a footing or mat when you want the shear reinforcement options. The Two-way slab, Spread footing and Pile cap types keep their own punching checks.

Inputs of the punching check #

• Column or loaded area: rectangular (c1 along x, c2 along y) or circular. For a circle choose the section: the exact circle at d/2 (22.6.4.1, the smallest perimeter, and the default), the square of equal area that 22.6.4.1.2 permits, or the square of equal perimeter of ACI 352.1R. Location: interior, edge (free edge on the −x side) or corner (free edges on the −x and −y sides), with the distance from the column face to each edge. The program takes the section that gives the smallest bo (22.6.4.1): it closes at d/2 where it fits, and runs to the edge otherwise. The sides that stay in the slab set αs (R22.6.5.3), so a column far from an edge counts as interior.
• Slab: thickness h, effective depth d (the average of the two directions, 22.6.2.1), f'c, λ, fy of the slab bars, and the size effect factor λs (Eq. 22.5.5.1.3). λs is on by default, because Table 22.6.5.2 requires it. Turning it off raises a warning: 13.2.6.2 allows that only for some shallow foundations. Drop panel or shear cap: its plan size and its projection below the slab. d at the column then includes the projection, and a second section is checked at the edge of the panel (22.6.4.1(b)).
• Factored loads: up to 20 cases of reaction and moments in x and y. A positive Mx raises the stress on the +x side, the side away from an edge, and a positive My the stress on the +y side. Mind the signs at edges and corners, where the two sides of the section differ. Moments entered at: the centroid of the critical section (R8.4.4.2.3, usual for program output) or the column centre, in which case the eccentricity of the reaction about the centroid is added. Factored load inside the section wu: subtracted from the reaction over the plan area inside each section; 0 takes the reaction as Vu, which is conservative.
• Shear reinforcement: none, stirrups or headed studs; the stud diameter or stirrup bar; rails or legs on each x face and each y face (running square to the face, evenly spaced between the insets from the corners, none across a free edge); s0, s, the number of peripheral lines, fyt (taken as at most 60,000 psi, 22.6.3.2; studs are commonly 51,000 psi, R20.4); and whether the studs are smooth with a shaft of 10 in. or less, one condition of λs = 1.0 (22.6.6.2(b)).
• Moment transfer and top bars: γf by Eq. 8.4.2.2.2, or modified by you with the net tensile strain εt; the program checks Table 8.4.2.2.4 for what you enter. Top bars within bslab, optional: when entered they are checked against Eq. 8.6.1.2.
• Openings: centre and size of up to 8. Those within 4h of the column reduce bo (22.6.4.3).

Auto-design varies the slab thickness (d follows, keeping the entered h − d) and, with shear reinforcement, the stud diameter or stirrup bar, the line spacing and the number of lines. The column, loads, f'c, openings and the rails on each face stay as entered.

Checks performed #

The drawings show the plan with the column, free edges, every section (dashed), openings with their ineffective part, the shear reinforcement as entered, and a section along a rail. The stud assembly and stirrup shape are not drawn.

Limitations #

• Prestressed slabs (22.6.5.5), shearheads, L-shaped and re-entrant columns and beams framing into the column are not covered.
• The section outside the reinforcement is the shortest line at d/2 from the outermost legs and the column, with rounded corners, which gives the smallest perimeter. It is conservative compared with a straight-sided polygon. ACI 421.1R-20 gives the polygon in detail; it is not on disk (see Verification).
• Moments act about the section's own x and y axes, as the published examples do, not about principal axes at a corner.
• At the outer section γv is the value of the section at the column (8.4.2.2.2 defines it there).
• Rails run square to the faces, not radially. For a circular column they start from the column's bounding square. Enter the layout your supplier gives by its rails on each face, and treat the outer section as an estimate if the real layout differs.
• Flexural design, integrity reinforcement (8.7.4.2) and the assembly height (8.7.7.1.1) are yours to check. Seismic drift limits on slab-column connections (18.14.5) are not checked.

Verification examples #

Verification status: 72 values compared in 16 examples (16 published, 0 hand calculations from the cited equations): 67 within tolerance, 5 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.

Published examples, written to ACI 318-14 except the last; below d = 10 in. the 318-19 size effect factor is 1.0, so the values carry over.

Three things to read with these. DE-PSC has no λs; the program's φvc at d = 10.3 in. is 0.7 % lower. DE-PSC prints 193.0 psi for a sum that is 192.0, and the program gives 191.9. The Dlubal page was read through a web page summary and does not say how its 10 studs per line sit on the faces; the outer section result rests on an assumed layout of 3 rails on each long face and 2 on each short one.

Stirrups and the drop panel section have no published example here: they are checked by behaviour tests against the code expressions. ACI 421.1R-20, whose stud examples would close that gap and confirm the outer polygon, is not on disk; only its preview is.