Problem 5.154 a 24 kN 30 kN The beam AB supports two concentrated loads and rests on soil which exerts a linearly distributed upward load as shown. Determine (a) the distance a for which wA = 20 kN/m, (b) the corresponding value wB. 0.3 m A B wA wB 1.8 m

Solving Problems on Your Own a 24 kN 30 kN 0.3 m The beam AB supports two concentrated loads and rests on soil which exerts a linearly distributed upward load as shown. Determine (a) the distance a for which wA = 20 kN/m, (b) the corresponding value wB. A B wA wB 1.8 m 1. Replace the distributed load by a single equivalent force. The magnitude of this force is equal to the area under the distributed load curve and its line of action passes through the centroid of the area. 2. When possible, complex distributed loads should be divided into common shape areas.

RII = (1.8 m)(wB kN/m) = 0.9 wB kN Problem 5.154 Solution a 24 kN 30 kN 0.3 m Replace the distributed load by a pair of equivalent forces. C A B 20 kN/m wB 0.6 m 0.6 m RI RII 1 2 We have RI = (1.8 m)(20 kN/m) = 18 kN 1 2 RII = (1.8 m)(wB kN/m) = 0.9 wB kN

SFy = 0: -24 kN + 18 kN + (0.9 wB) kN - 30 kN= 0 or wB = 40 kN/m Problem 5.154 Solution a 24 kN 30 kN 0.3 m C A B wB 0.6 m 0.6 m RI = 18 kN RII = 0.9 wB kN (a) + SMC = 0: (1.2 - a)m x 24 kN - 0.6 m x 18 kN - 0.3m x 30 kN = 0 or a = 0.375 m (b) + SFy = 0: -24 kN + 18 kN + (0.9 wB) kN - 30 kN= 0 or wB = 40 kN/m