Question

4 m 1.5 m 2 m 2 m 2 m 2 m Figure 1: Loaded truss The truss ilustrated in figure 1 is loaded by a vertical load P at E as illus a) Find the vertical displacement in the trus at point E us enerey AE is constant in alf the bars of the truss. ing the prinsipal of minimum potential he vertical displacement of point E if all the bars have a diameter of D 0 GPa and a load P-10 kN is applied. 10 cm, modulus of elasticity of 20o

Answer 1

Consider the figure 4 m .5 m 2 m 2 m 2 m 2 m Calculate the angle α α 36.870 Calculate the strain in bar AE Lu Lu 0.25u Calculate the strain in bar BE.

sin 36.87 Cos 36.87 4(cos 36.870) , uy (Sin 36.870) 1.5) +(2 0.32u, +0.24u Calculate the strain in bar EC. cos 36.870 E3 4, (cos 36.87°) 1.5) +(2 --(0.3214 + 0.244) Calculate the strain in bar ED --0.25u Calculate the total potential energy of the system.

..!( (f1.5)24(2)2) 0.2%)2 (4)-(0.32m +0.24 u.). 1 -(-(0.32«, + 0.24u.)). (yl 1.5), + (2)') + (-0.2%) (4) EA (025) 4u+(0.32) u(25) (024 (25)+2032)024)(25u--, = EA [050642 +0.144u,' + 0.384u&J-Fu,-F,«,

Apply the principle of minimum potential energy OU ou, (EA0.50бы. + 0.144«,, +0.38444 ]-Fur-Fu.):0 1.012u, +0.384u 1.012ux +0.38415 =(0) EA 1.012u, +0.384u0 u,--0.37%. Apply the principle of minimum potential energv

OU Ou EA 0.506u+0.144u+0.384u,u EA LO +0.288«, +0.384«J-o-F, 。 0.288«, +0.384«, EA Substitute the given values 0.288u +0.384u x EA 0.288m + 0.384(-0.37%, EA 7.02P EA Calculate the vertical displacement of point E. 7.02P EA 7.02(10x10') 200 x 109)| 쯔 0.102 4.469 x10 m