Sketch a grillage beam element, 1-2. Label the local axes and indicate clearly the actions at each node. 3 Marks (e) Software output from a grillage analysis for an edge beam member 1-2, of length 9m is to be checked. The nodal actions at node 1 are given as: Qz= -100 kN, My= 0 kNm and Tx = 20 kNm. Using the global Cartesian co-ordinate system x, y, z, with the member 1-2 in the x direction, the loading on the beam is as follows: A uniformly distributed load of 3 kN/m applied eccentrically at a distance of 1.0m (counter-clockwise direction node 1 to 2). A point load of 10 kN positioned 2.0m from node 1 and at an eccentricity of 1.5 m (in clockwise direction node 1 to 2). A uniformly distributed load of 20kN/m applied directly through the shear centre of the beam. Beam 1-2 is subject to a torsion of 5 kNm acting at the middle of the section and rotating in a clockwise direction node 1 to 2.
i) Determine all the actions at node
(ii) Sketch the shear force diagram for the beam indicating all principal values.
(iii) Sketch the bending moment diagram for the beam indicating all principal values.
(iv) Sketch the torsion moment diagram for the beam indicating all principal values.