Question

Q.2: For the grillage shown in the figure, evaluate the n the structure taking same modulus of elasticity (E-200GPa) and Poisson's ratio (v 0.25) for all members [calculate shear modulus G from E and v [G-E(2(1 + v))). The members are having same rectangular cross-section of 50 mm x 80 mm (depth). Use the attached table to calculate the torsional constant J (Note: J is not equal to the polar moment of inertia which is applicable for a non-circular section only) of the members. oad vector and the stiffness matrix o Addition learning materials ttps://en.wikipedia.org/wiki/Torsion(mechanics https://en.wikipedia.org/wiki/Young%.27s moduļus 40 kN 2.5m AB BD-5m BC-BE-2.5m 3kN/m Horizontal plane: X-Y The torsional constant (J) of a member having a rectangular section (axb, b>a): J-ka'b Table of Constants for Torsion of a Rectangular Bar 1.00.675 1.20.759 1.5 0.848 0.1406 0.166 0.196 0.208 0.219 0.231 24 30.985 0.997 0.999 0.263 0.281 0.291 0.267 0.282 0.291 The torsional constant (J) of a member having a rectangular section (axb, b>a): J-ka'b Table of Constants for Torsion of a Rectangular Bar 1.00.675 1.20.759 1.5 0.848 2.0 0.930 2.50.968 0.1406 0.166 0.196 0.208 0.219 0.231 0.246 0.258 30.985 0.997 0.999 1.000 1.000 0.263 0.281 0.291 0.312 0.333 0.267 0.282 0.291 0.312 0.333 4 10 0.249 The table is taken from "Theory of Elasticity, 3rd Edition, S.P. Timoshenko and J.N. Goodier"

Answer 1

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