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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 truss and virtual truss. Thank you. You may use the other picture for guide.

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. L = length 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. L = length 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.
What is the horizontal displacement at Joint B in mm? A=500 mm² and E-200 GPa What is the vertical displacement at Joint 8 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 8 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
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