000_[Jonathan_Ochshorn]_Structural_Elements_for_Architecture_400

336 APPENDIX 8 Tables for Chapter 8 (beams)

Table A-8.5 (Continued)
D. Available moments from 400 to 600 ft-kips

(Continued )

Tables for Chapter 8 (beams) 337

Table A-8.5 (Continued)
E. Available moments from 600 to 1000 ft-kips

(Continued )

338 APPENDIX 8 Tables for Chapter 8 (beams)

Table A-8.5 (Continued)
F. Available moments from 1000 to 2000 ft-kips

(Continued )

Tables for Chapter 8 (beams) 339

Table A-8.5 (Continued)
G. Available moments from 2000 to 5000 ft-kips

(Continued )

340 APPENDIX 8 Tables for Chapter 8 (beams)

Table A-8.5 (Continued)
H. Available moments from 5000 to 10,000 ft-kips

Notes:

1. Values are based on the conservative assumption that the “lateral-torsional buckling modifier,” Cb ϭ 1.0.
This conservative value of Cb ϭ 1.0 is quite close to the actual value for simply supported beams with equally
spaced point loads of equal weight, where the beam is braced at those points only, except for the special

case of a single point load at midspan, in which case Cb ϭ 1.364. Actual values for Cb can be found for each
unbraced beam segment by calculating the bending moments at the quarter-points along each segment (MA,
MB, and MC, with MB being the moment at the midpoint of the segment), as well as the maximum moment,
Mmax, within each segment, and then inserting these values into Equation 8.13, reproduced as follows:

Cb ϭ 12.5Mmax ≤ 3.0
2.5Mmax ϩ 3MA ϩ 4MB ϩ 3MC

In any case, the available moment cannot exceed Mp/Ω, the value for braced, compact sections given in Table A-8.4.
2. Solid circles represent the maximum unbraced length, Lp, for which a plastic moment can be achieved
before the onset of lateral-torsional buckling; open circles represent the maximum unbraced length, Lr, for
which an elastic moment can be achieved before the onset of lateral-torsional buckling (see Figure 8.24).

Tables for Chapter 8 (beams) 341

Table A-8.6 “Shear” equations for reinforced concrete beams1

A. Capacity of steel stirrups2 (lb) Vs ϭ 2Asf y d
s

B. Required stirrup spacing2 (in.) s ≤ 2Asfyd
Vs

C. Capacity of concrete3 (lb) Vc ϭ 2bd fcЈ

D. Strength design equation2 Vu ≤ φ(Vc ϩ Vs )

E. Required steel capacity (lb) from strength design Vs ≥ Vu Ϫ Vc
equation2 φ

F. Maximum stirrup spacing3 (in.) For Vs ≤ 2Vc, the smaller of:
● d/2
● 24 in.
● 2Asfy /(50b)

For Vs > 2Vc, the smaller of:
● d/4
● 12 in.
● 2Asfy /(50b)

G. Design shear where no stirrups are needed2 (lb) Vu ϭ 0.5φVc

Notes:

1. Units are as follows:

b ϭ cross section width (in.)
d ϭ cross section effective depth (in.)
s ϭ stirrup spacing (in.)
As ϭ stirrup bar area, one “prong” only (in.2)
fy ϭ yield stress of steel stirrup (psi)
fcЈ ϭ cylinder strength of concrete (psi)
Vu ϭ design (factored) shear force (lb)
Vc ϭ capacity of concrete to resist shear (lb)
Vs ϭ capacity of steel stirrups to resist shear (lb)
φ ϭ 0.75 for shear (see Table A-5.2)

2. Units specified for lb and psi units according to Note 1 may be changed to kips and ksi in these equations

only.

3. The concrete cylinder strength fcЈ must be in psi units in Table 8.6, part C (with the resulting value of Vc in lb
units), and the steel yield stress fy must be psi units in part F (with in. units resulting).