MEM427_HW_1_Solution

# MEM427_HW_1_Solution - MEM427 HWAssignment#1Solutions...

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MEM427 HW Assignment #1 Solutions Fall 2010 1 / 4 Homework Assignment #1(a) A truss made from Douglas fir wood is subjected to an inclined force of P = 400 lb at joint A as shown in the figure. Each member has a cross sectional area of 8.0 in 2 and a modulus of elasticity of E = 1.90 x 106 lb/in 2 . Determine the displacements at joint A ( A u and A v ) and the forces in all members by using the stiffness method. Solution: A B A u A v A P = 400 lb AB S 45 AC S AD S Fig. 1 Elongation of member AB Fig.2 F.B.D. of joint A First, express the elongation of each member in terms of the joint displacements. Of the four joints in this truss, only joint A is free to move while joints B , C , and D are fixed. Let the horizontal and vertical displacements of joint A be A u and A v , respectively. The elongation of member AB can be expressed in terms of A u and A v (see Fig.1) as A A A A AB v u v u 8 . 0 6 . 0 sin cos where, as ABC being a 3:4:5 triangle, 13 . 53 5 . 1 0 . 2 tan 1 8 . 0 13 . 53 sin sin 6 . 0 13 . 53 cos cos Similarly, for members AC and AD , where 90 and 6 . 116 , respectively, we have A A A AC v v u 90 sin 90 cos A A A A AD v u v u 894 . 0 447 . 0 6 . 116 sin 6 . 116

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## This note was uploaded on 11/14/2010 for the course MEM 427 taught by Professor Tein-mintan during the Fall '10 term at Drexel.

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MEM427_HW_1_Solution - MEM427 HWAssignment#1Solutions...

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