Question

The cross-sectional area of each member of the truss shown in the figure is 4 = 400 mm and E = 200 GPa. (a) Determine the vertical displacement of joint Cif a 4-KN force is applied to the truss at C. (b) If no loads act on the truss, what would be the vertical displacement of joint C if member AB were 5 mm too short? (c) If 4 kN force and fabrication error are both accounted, what would be the vertical displacement of joint C. 3 m 4 KN 4 m 4 m

Answer 1

yen for Reactions, EMA=0 니 VB x 8 = 4x3 A 06 VB = 1 2 = 1.5kN (1) k -yom you VA -1.5KN (V)

At Joint A FACsino-15=0 FAC = 1.5x5 - 2.5KN (T) NOW FACCOSO - +FAB=4 3 FAB=4 - 25 x 4 = 2100 (7)

2X3 AO 1 gard FBc sino tis=0 FBC = -2.510 (c) Now for unit force at Joint A FACsino t=0 FACE 185 --0-833 kN (6) Now, FACCESOTHAB=0 FAB = -[-0-833x4] 0.67 kN (T) Now, at Joint B FBC sino th=0 FBC = -0.8333NCC) (Q)... vertical displacement = suil Pili Altij here, ui= force in the ith member due to unit force R-force in the ith member due to esternike loading (4) Li- leangth of member ith

: Ove = EUABLAR 0.67X5 3.35mm (V)

Ovo (c.conen both load and fabrication error occure, Vc = {uilt Pili Ove = UAB (PABLAR to tulac AE AF AE (2x 8000 67 -2.5x5000 -0.833 200x you орхчер + i) - [o 57 -0-833/2.5X5000 t 900X400 = 3.484 mm