load lumping H R T 01

Dimensions:

a	b	c	$w_1$	$w_2$	$w_3$
3.6 ft	5.6 ft	3.1 ft	3.6 kip/ft	1.9 kip/ft	3.4 kip/ft

Problem Statement:
The load applied between A and B has the profile of a quarter circle. For the dimensions and load values given above, find:
$\bullet$  the magnitude of the overall force applied to the beam, and,
$\bullet$  the x location where the overall distributed load may be concentrated so as to cause the same support reactions.

Answers:
$F_{lumped}$ =
$x_{lumped}$ =

be sure to include units with your answers