Question

For the three truss structures given below, determine the joint displacements at the location and in the directi indicated. Give displacement results in terms of A and E. For example, 550/(AE). For the third truss proble Member AG has twice the cross-sectional area of all other members in the truss and three times larger modul of elasticity (made of a different material).

Answer 1

Consider the given truss is 100 kips 100 kips 9 ft 60 kips 3@10 ft 30 ft 30 kips So r

RA2 100 kips 100 kips RA1 9 ft RH 60 kips 3@10 ft 30 ft 30 kips Consider equilibrium condition Rn +30+60 100 +100 R2 200-90 R2110kips

Taking moment at point A R x930x1060x 20 100x10 +100x 20 9R 3000-1500 9R 1500 1500 R, 166.67kips R 166.67kips R--166.67kips 13.345FIT 9FIT 41.98DG 10FIT

Considered point H Suppose that tension force in member HG is Fo and tension force in member in HA is Fz. Consider equilibrium condition at point H is RgF-166.67kips НА Considered point A Suppose that tension force in member AB is Fs and tension force in member in AH is F. in member AG is F AG Consider equilibrium condition at point A is

0 F 0.743FG 166.67 kips FAH+110+FAG COS 48-0 0+0.669FA-110kips 110 G0.669 --164.42kips Substitute the value of FG in equation (G) FAB +0.743x-164.67 166.67kips F. 288.8kips

Considered point G Suppose that tension force in member GH is FGH tension force in member in GA is Fe n member GB is F and member GF is FoF Consider equilibrium condition at point H is -166.67 kipsFo 164.42 cos 41.980 Fo44.44kips 30 F sin 41.98FB0 30-166.67 sin 41.98+FG0 FB 8148kips