Calculate the vertical displacement of joint B using the virtual work method. Each bar is made of A-36 steel and has a cross-sectional area of 1.5 in2 as shown in Figure 1. The Young's modulus of the material is 29,000 ksi.

SOLVES STEP BY STEP, USE TABLE IF NECESSARY

3 The piece of plastic is originally rectangular. Calculate the shear strain Yxy at corners A and B if the plastic distorts as shown by the dashed lines. 2 mm 300 mm 2 mm D -400 mm- mm, B A 4 mm 72 mm 3 mm X

Figure Q4 shows a piece of triangular thin plate ABC with thickness 5 mm. A linear pressure as shown in the figure is being applied to edge AB with maximum intensity of 100 kN/m² at the middle of edge AB. The plate is made from stainless steel, with a Young's modulus of 200 GPa and Poisson's ratio of 0.3. The deformations in the plate are to be obtained. For such purposes, the finite element method is being employed. (a) (b) (c) (d) (e) State the type of problem involved in this case (to determine the stiffness matrix to be used). Model this problem optimally using the least number of orthogonal triangular elements only. Label the nodes and elements and indicate clearly the status of all the relevant degrees-of- freedom in this model. Set up the appropriate system of simultaneous equations and solve for the unknown displacements. Displacements at point T. Without any calculation, explain on the value of strain at points S and T.

The plate has a thickness of 20 mm and the force P = 5 kN acts along the centerline of this thickness such that d = 150 mm. (Figure 1) Figure d‡ 200 mm a 1 of 1

The cross-sectional dimensions of a beam are shown in the figure. (a) If the bending stress at point K is 35 MPa (C), determine the internal bending moment Mz acting about the z centroidal axis of the beam. (b) Determine the bending stress at point H. The bending stress is positive if in tension and negative if in compression. 85 mm 4 mm TT K 55 mm H 4 mm 45 mm 4 mm Answers: (a) Mz = UN-m (b) OH = JMPA

A thin rectangular plate ABCD is deformed into a parallelogram as shown in the figure below. The width of the plate is w = 1400 mm, and the height of the plate is h = 1900 mm. The shear strain at A is known to be +4294 μrad. Assume a = 2.4 mm. Calculate the magnitude of dimension b in the figure. D h Answer: b= i A W Ta mm 2