**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

^{-4}m

^{2}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

**= 25mm. Assume the element nodal displacement have been determined to be u**

*t*_{1}=0.0mm, v

_{1}=0.0635mm, u

_{2}=0.03048mm,v

_{2}=0.0mm,u

_{3}=0.0mm, and v

_{3}=0.0635mm.Determine the element stresses.

__Fig: 04__