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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