2D Frame I
Calculate deformation of node 4 of the isostatic system below, using the Virtual Work Method manually.
![](../__attachments/1963754383/image-20210712-085318.png?inst-v=5c738f36-5d0a-4235-b600-0cef56c14e9d)
Hint for solution
According to the method; Integral should be considered separately for bars between 1-2 and 2-4 nodes.
Detailed solution
E= Modulus of elasticity A= Cross-sectional area I= Cross-section moment of inertia M= Moment on the element due to external loading M'= Moment on the element due to unit loading Δ= Deformation
Step 1: Finding Moment Function Based on Unit Load
![](../__attachments/1963754383/image-20210712-090208.png?inst-v=5c738f36-5d0a-4235-b600-0cef56c14e9d)
1: Unit loading D1 , D2 , D3 : Support responses M12 : 1-2 bars 2 DN moment value M24 : 2-4 bars 2 DN moment values L12 : 1-2 bars length L24 : 2- Length of 4 bars M12 (x): 1-2 bars Moment function
M24 (x): 2-4 bars Moment function ΣM1,dn : Total moment about 1 DN ΣM4,dn: Total moment about 4 DN
ΣD: Total equilibrium
![](../__attachments/1963754383/durum%201D.png?inst-v=5c738f36-5d0a-4235-b600-0cef56c14e9d)
Moment Function : ,
Step 2: Finding the Moment Function Based on the Given Load
![](../__attachments/1963754383/image-20210712-091237.png?inst-v=5c738f36-5d0a-4235-b600-0cef56c14e9d)
D 4 , D 5 , D 6 : Support responses M'12 : 1-2 bars 2 DN moment value M'24 : 2-4 bars 2 DN moment values L12 : 1-2 bars length L24 : 2-4 bars length M'12 (x): 1-2 bars moment function M'24 (x): 2-4 bars moment function ΣM 1,dn : 1 Total moment relative to DN ΣM4,dn: 4 Total moment relative to DN ΣD: Total equilibrium
Moment Function :,
Step 3: Multiplying the M and M' Moment Functions in the Previous Steps and Getting the Integral
Integral for 1-2 Bar
Integral for 2-4 Rod
Deformation of node 4 = 0.095 m
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