gershoe.blogg.se - Principle of virtual work structural analysis examples

Since the vertical displacement of joint C is to be determined, only a vertical 1 kN load is placed at joint C. (b) If no loads act on the truss, what would be the vertical displacement of joint C if member AB were 5 mm too short? (c) If 4 kN force and fabrication error are both accounted, what would be the vertical displacement of joint C.ġ kN -2.5 +2.5 -0.833 -0.833 4 kN 2 0.667 0 0.5 kN 0.5 kN 1.5 kN C 1.5 kN 4 kN C A B B A n (kN) N(kN) SOLUTION Part (a) (a) Determine the vertical displacement of joint C if a 4-kN force is applied to the truss at C. Fabrication Errors and Camber Where: D = external joint displacement caused by the fabrication errors DL = difference in length of the member from its intended size as caused by a fabrication errorĬ 4 kN 3 m A B 4 m 4 m Example 8-15 The cross-sectional area of each member of the truss shown in the figure is A = 400 mm2 and E = 200 GPa.Temperature Where: D = external joint displacement caused by the temperature change a = coefficient of thermal expansion of member DT = change in temperature of member Where: 1 = external virtual unit load acting on the truss joint in the stated direction of D n = internal virtual normal force in a truss member caused by the external virtual unit load D = external joint displacement caused by the real load 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 P1 n1 N1 P2 n6 N6 N4 n4 N2 n2 n3 N3 n5 N5 B B n7 n8 n9 N7 N8 N9 D 1kN Method of Virtual Work : Truss U L Virtual loadings Virtual loadings u A Real displacements Real displacements P´ = 1 Apply virtual load P´ first u L u A dL D P1 Then apply real load P1. P L M diagram P M -PL x V x SMx= 0: + Principle of Work and Energy

Strain Energy-Shear For reference: Strength of Material by Singer, Fourth Edition, -163.

Strain Energy-Torsion dx For reference: Strength of Material by Singer, Fourth Edition, -68.

M ´ + M Eigen work M M Displacement work dq M q q´ q -(8-12) Eigen work -(8-13) -(8-14) As the magnitude of F is gradually increased from zero to some limiting value F = P, the final elongation of the bar becomes D.į ´ + P Eigen work P F Displacement work D D´ D´ x P D L L F´ (Ue)Total = (Eigen Work)P + (Eigen Work)F´ + (Displacement work) PĢ0 kN Eigen work 15 kN F Displacement work 0.75 cm 0.0075 0.01 0.25 cm x (m) 15 kN L L L 0.75 cm 5 kN 15 kN

Deflection: Virtual Work Method Trusses Theory of Structure - Iį L P Eigen work Ue D x D F Eigen work External Work and Strain Energy Most energy methods are based on the conservation of energy principle, which states that the work done by all the external forces acting on a structure, Ue, is transformed into internal work or strain energy, Ui.