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truss deflection - Page 1 M9 Truss Deflections and...

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Page 1 M9 Truss Deflections and Statically Indeterminate Trusses TRUSS DEFLECTION EXAMPLE Calculate deflection of loading point E in pin-jointed truss shown below. Bars are at 90 ° or 45 ° to each other. All bars have cross sectional area A, Young's modulus E. No temperature change occurs. Draw FBD Â F y ↑= 0 V A - P = 0 fi V A = P (1) Æ Â F x = 0 : H A + H B = 0 H A = - H B (2) M A = 0 : H B L - 2 LP = 0 Â H B = 2 P fi H A = - 2 P
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Page 2 Analyze bar forces. Mo J. @B Â F y ↑= 0 F BA = 0 Æ Â F x = 0 : F BD + 2 P = 0 fi F BD = - 2 P @E Â F y ↑= 0 : F EC Sin 45 o - P = 0 fi F EC + P 2 Æ Â F x = 0 : - F EC Cos 45 o = 0 - F ED fi F ED = - P H A V A = 0 : + 2 PL - PL - F AC L = 0 M D Â Â F fi F AC = + P V V A y ↑= 0 : F DC + P = 0 fi F DC = - P V A Â F y ↑= 0 : P - F AD Cos 45 o = 0 fi F AD = 2 P
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Page 3 FL Bar Deflections given by AE Bar Force/P Length/L d FL AE ( ) AB 0 1 0 BD -2 1 -2 AD + 2 2 2 AC +1 1 +1 CD -1 1 -1 DE -1 1 -1 CE + 2 2 + 2 Deflection Diagram: 1. Fixed points - 0, A, B 2. Locate D ' via extension/rotations of BD & AD 3. Locate C ' via extensions/rotations of AC & CD 4. Locate E ' via extensions/rotations of CE & DE
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