Page 61 - Handbook of Civil Engineering Calculations, Second Edition

1.44 STRUCTURAL STEEL ENGINEERING AND DESIGN

FIGURE 27

Calculation Procedure:

1. Place full load on the overhangs, and compute the
negative moment
Refer to the moment diagrams. For every position of the supports, there is a correspon-
ding maximum bending stress. The position for which this stress has the smallest value
must be identified.
As the supports are moved toward the interior of the beam, the bending moments be-
tween the supports diminish in algebraic value. The optimal position of the supports is
that for which the maximum potential negative moment M 1 is numerically equal to the
2
2
maximum potential positive moment M 2 . Thus, M 1 1.2w(x /2) 0.6wx .
2. Place only the dead load on the overhangs and the full load
between the supports. Compute the positive moment.
Sum the areas under the shear diagram to compute M 2 . Thus, M 2 /2[1.2w(L/2 x)
2
1
2
2
2
0.2wx ] w(0.15L 0.6Lx 0.5x ).
3. Equate the absolute values of M 1 and M 2 and solve for x

2
2
2
Substituting gives 0.6x 0.15L 0.6Lx 0.5x ; x L1 0.5 0.5 3) 0.240L.
FLEXURAL CAPACITY OF A COMPOUND BEAM
A W16 45 steel beam in an existing structure was reinforced by welding a WT6 20
to the bottom flange, as in Fig. 28. If the allowable bending stress is 20,000 lb/sq.in.
(137,900 kPa), determine the flexural capacity of the built-up member.