Handbook of Civil Engineering Calculations

The shear factor equals the ratio of

the average width of the adjacent aisles

to the total width. Or, line A 9 15/75 =

0.20; line B, (15 + 12)775 = 0.36; line C,

(12 + 10.5X75 = 0.30; line D 9 10.5/75 =

0.14. For convenience, record these val-

ues in Fig. 15.

2. Compute the shear
   in each column
   (b) For instance, column A-2-3, H =
   -3900(0.20) = -780 Ib (-3.5 kN); col-

FIGURE (^16) umn Ci1-2, H = -(39OO + 7500)0.30 =
-3420 Ib (-15.2 kN).

3. Compute the end moments
   of each column
   Apply Eq. c. For instance, column A-2-3, M= /2(-78O)IS =-5850 ft-lb (-7932.6 N-m); column
   Z)-O-I, M= /2(-275I)IS = -24,759 ft-lb (-33,573.2 N-m).


4. Compute the end moments of each beam
   Do this by equating the algebraic sum of end moments at each joint to zero. For instance,
   at line 3: MAB = 5850 ft-lb (7932.6 N-m); MBC = -5850 + 10,530 = 4680 ft-lb (6346.1
   N-m); MCD = -4680 + 8775 = 4095 ft-lb (5552.8 N-m). At line 2: MAB = 5850 + 17,100 =
   22,950 ft-lb (31,120.2 N-m); MBC = -22,950 + 30,780 + 10,530 = 18,360 ft-lb (24,896.0
   N-m).


5. Compute the shear in each beam
   Do this by applying Eq. b. For instance, beam B-2-C, V= 2(18,360)724 = 1530 Ib (6.8
   kN).


6. Compute the axial force in each member
   Do this by drawing free-body diagrams of the joints and applying the equations of equi-
   librium. It is found that the axial forces in the interior columns are zero. This condition
   stems from the first assumption underlying the portal method and the fact that each interi-
   or column functions as both the leeward column of one portal and the windward column
   of the adjacent portal.
   The absence of axial forces in the interior columns in turn results in the equality of the
   shear in the beams at each tier. Thus, the calculations associated with the portal method of
   analysis are completely self-checking.

WIND-STRESS ANALYSIS

BY CANTILEVER METHOD

For the bent in Fig. 17, calculate all shears, end moments, and axial forces induced by the

wind loads by applying the cantilever method of wind-stress analysis. For this purpose,

assume that the columns have equal cross-sectional areas.

Calculation Procedure:

1. Compute the shear and moment on the bent at midheight
   of each horizontal row of columns
   The cantilever method, which is somewhat more rational than the portal method,