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VirtualWork Truss

# VirtualWork Truss - Static Equilibrium Equations MA=0-2020...

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Ay Dy Dx MA=0: -2020+Dy15=0 Dy=26.67kips up MB=0: 2020+26.6715+Dx20=0 Dx=40kips left FY=0: Ay=26.67kips (down) Joint A Equilibrium: 20+a(15/25)=0 a= -33.33 (c) b-33.33(20/25)-26.67=0 b= 53.33 (t) Joint B Equilibrium: -53.33-a(20/25)=0 a= -66.66 (c) 20-66.66(15/25)+b=0 b= 19.99 (t) Joint C Equilibrium: 33.33(20/25)-a=0 a= 26.66 (t) 26.67 40 26.67 53.33 26.66 -33.33 -66.66 19.99 26.67 26.67 MD=0: Ay=0 Fy=0: Dy=0 Fx=0: Dx=1kips (left) Joint A Equilibrium: 1+a(15/25)=0 a= -5/3 (c) -5/3(20/25)+b=0 b= 4/3 (t) Joint B Equilibrium: -4/3-a(20/25)=0 a= -5/3 (c) -5/3(15/25)+b=0 b= 1 (t) Joint C Equilibrium: 5/3(20/25)-a=0 a= 4/3 (t) -5/3 1 4/3 4/3 -5/3 1 1 -1.97 Static Equilibrium Equations: Fx=0:20+20-21.97-Dx=0 Dx=18.03kips (left) Joint A Equilibrium: 20-21.97+a(15/25)=0 a= 3.28 (t) 3.28(20/25)-26.67+b=0 b= 24.04 (t) Joint B Equilibrium: -24.04-a(20/25)=0 a= -30.05 (c) 20-30.05(15/25)+b=0 b= -1.97 (c) Joint C Equilibrium: -3.28(20/25)-a=0 a= -2.62 (c) 18.03 26.67 21.97 26.67 -2.62 3.28 -30.05 24.04 26.67 26.67 26.67 Problem: Given the following truss system, compute the reactions and internal forces using the Virtual Work method. Solution: Notice that a distributed load is applied to the left vertical truss member. To simplify calculations, we will first create an idealized model.

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