3- Let the density of the pyramid material be p = 2000 kg/m. Determine the average normal stress at a cross section located at x measured from the apex. Express the stress as a function of x. Assume g = 9.81 m/s. Hints: Weight has a unit of force and equals mg where m denotes the mass. The volume of a pyramid is V = lwh/3. Mass is as M = pV. (2 Pnts) 4- 50 m 20 m h h 20 m A bar is made of a metal with a tensile strength of 80 MPa. (a) Calculate the minimum cross-sectional area of the bars such that the truss can withstand the load shown. Assume a factor of safety as S.F=1.6. (b) If the joint between the members is as shown, determine the average shear stress in the pin of the lap joint. (2 Pnts) NAC 4 m 20 KN 20 KN 3 m N AB D-10 mm 1- For the splice joint shown the dimensions are L = 20 mm and W = 10 mm. Note that the lap length is L/2 for each side of the joint. (a) Determine the maximum tensile force if the shear strength of the glue is ultimate = 10 MPa. (b) Assume a factor of safety as S.F = 1.5 and calculate the allowable magnitude of the load. (2Pnts) P L-2L-2 W P 2222 P P 2- Two pieces of timber are to join using a dowel joint. The entire surface of the joint is glued as shown. If the tensile and shear strengths of the glue are 15 MPa and 10 MPa respectively, calculate the maximum tensile load that the joint can withstand. Assume that the bases of the dowels are not glued. Also, assume that the normal stress on the flat surface and the shear stress on the surfaces of the dowels simultaneously attain their maximum values. (2 Pnts) P 20 mm: P 150 mm 10 mm 10 40 mm 20mm