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Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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 Please answer the following and fill up the table using Principle of virtual work method only. Please draw an fbd on real & virtual truss. You may use the other picture for guide the formulas are provided. Thanks

What is the horizontal displacement at Joint B in mm? A=500 mm² and E-200 GPa What is the vertical displacement at Joint B in mm? A=500 mm² and E= 200 GPa MEMBER AB AC BC BD CD LENGTH 3√2 3 3 5 4 N(KN) Nx NXNL 33 kN B AE (mm) 3 m 9 kN Ny 3m C 4m NYNL AE (mm) D
Transcribed Image Text:What is the horizontal displacement at Joint B in mm? A=500 mm² and E-200 GPa What is the vertical displacement at Joint B in mm? A=500 mm² and E= 200 GPa MEMBER AB AC BC BD CD LENGTH 3√2 3 3 5 4 N(KN) Nx NXNL 33 kN B AE (mm) 3 m 9 kN Ny 3m C 4m NYNL AE (mm) D
Method of Virtual Work-Truss (due to external Loadings) B Apply virtual unit load to B (a) P₂ Apply real loads P₁, P₂ nNL AE 1· Δ = Σ" where 1 = external virtual unit load acting on the truss joint in the stated direction of A. n = internal virtual normal force in a truss member caused by the external virtual unit load. A = external joint displacement caused by the real loads on the truss. N = internal normal force in a truss member caused by the real loads. Llength of a member. A = cross-sectional area of a member. E = modulus of elasticity of a member. Method of Virtual Work-Truss (due to Temperature) 1· Δ = Σπα ΔΤ L Where 1 = external virtual unit load acting on a truss joint in the stated direction of displacement A. n = internal virtual normal force in a truss member caused by the external virtual unit load. A = external joint displacement caused by the temperature change. a = coefficient of thermal expansion of member. AT = change in temperature of member L = length of member. Method of Virtual Work-Truss (due to Fabrication Errors and Camber) 1· Δ = Ση ΔΕ Where: 1 = external virtual unit load acting on a truss joint in the stated direction of displacement A. A = external joint displacement caused by fabrication error. n = internal virtual normal force in a truss member caused by the external virtual unit load. AL = difference in length of the member from its intended size as caused by a fabrication error.
Transcribed Image Text:Method of Virtual Work-Truss (due to external Loadings) B Apply virtual unit load to B (a) P₂ Apply real loads P₁, P₂ nNL AE 1· Δ = Σ" where 1 = external virtual unit load acting on the truss joint in the stated direction of A. n = internal virtual normal force in a truss member caused by the external virtual unit load. A = external joint displacement caused by the real loads on the truss. N = internal normal force in a truss member caused by the real loads. Llength of a member. A = cross-sectional area of a member. E = modulus of elasticity of a member. Method of Virtual Work-Truss (due to Temperature) 1· Δ = Σπα ΔΤ L Where 1 = external virtual unit load acting on a truss joint in the stated direction of displacement A. n = internal virtual normal force in a truss member caused by the external virtual unit load. A = external joint displacement caused by the temperature change. a = coefficient of thermal expansion of member. AT = change in temperature of member L = length of member. Method of Virtual Work-Truss (due to Fabrication Errors and Camber) 1· Δ = Ση ΔΕ Where: 1 = external virtual unit load acting on a truss joint in the stated direction of displacement A. A = external joint displacement caused by fabrication error. n = internal virtual normal force in a truss member caused by the external virtual unit load. AL = difference in length of the member from its intended size as caused by a fabrication error.
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