Sample Problem· Given: tension/compression rigidities E,A, = E2A2 = EA,E,A3, external load F. Find: internal forces in bars.? Solution:32αα/1. Make the truss determinate byreplacing extension/contractionrestraint along Bar 3 with Fn3AF2. Static equilibrium at joint AHVV3FN2NZF =0→ Fm = Fn2ZF, = 0=→(Fn1 +Fn2)cosα+Fn3 =)AAF16
• Given: tension/compression rigidities E1A1 = E2A2 = EA, E3A3 , external load F. Find: internal forces in bars. 1. Make the truss determinate by replacing extension/contraction restraint along Bar 3 with FN3 F A 1 3 2 l 1 2 1 2 3 0 0 ( )cos x N N y N N N F F F F F F F F A F F FN3 N1 FN2 Sample Problem • Solution: 2. Static equilibrium at joint A 16
3. Displacement compatibility at joint ADue to symmetry324l, = △l,αα7, = l, cos αN4. Displacement-force relationshipFniFn3lNl, =△l, =EAcosαE,A117
4. Displacement-force relationship 3. Displacement compatibility at joint A Due to symmetry 1 2 l l l 1 l 3 cos 1 1 cos F l N l EA 3 3 3 3 E A F l l N A 1 3 2 l A* 17