Engineering Mechanics

Tutorial
1. A positive shear force V_y =30N acts on the thin cross sections shown in Fig: 1. determine the shear flow along the centrelines and sketch it.
Fig: 01
2. For the spring assembly shown in Fig: 02, determines the nodal displacement, the force in each element, and the reactions. Use the direct stiffness method for the problem.

Fig: 02

3. For the two-bar truss shown in Fig: 03, determine the displacement in the y direction of node 1 and the axial force in each element. A force of P =1000kN is applied at node 1 in the positive y direction while node 1 settles an amount δ=50mm in the negative x-direction. Let E=210GPa and A=6.00x10^-4m² for each element. The length of the elements are shown in Fig: 03

Fig: 03
4. Evaluate the stiffness matrix for the element shown in Fig: 04. The coordinates are shown in units of millimetre. Assume plane stress conditions. Let E=210GPa, ν = 0.25, and thickness t = 25mm. Assume the element nodal displacement have been determined to be u₁=0.0mm, v₁=0.0635mm, u₂=0.03048mm,v₂=0.0mm,u₃=0.0mm, and v₃=0.0635mm.Determine the element stresses.

Fig: 04