The doubly-symmetric beam cross section shown in Figure P12.3b has been proposed for a short foot bridge. The cross section will consist of two identical steel pipes that are securely welded to a steel web plate that has a thickness of t = 9.5 mm. Each pipe has an outside diameter of d = 70 mm and a wall thickness is 5 mm. The distance between the centers of the two pipes is h = 370 mm. Internal forces of P = 13 kN, V = 25 kN, and M = 9 kN·m act in the directions shown in Figure P12.3a. Determine the stresses acting on horizontal and vertical planes: (a) at point H, which is located at a distance of yH = 120 mm above the z centroidal axis. (b) at point K, which is located at a distance of yK = 80 mm below the z centroidal axis. Show the stresses on a stress element for each point. FIGURE P12.3a FIGURE P12.3b P12.5 An extruded polymer flexural member is subjected to an internal axial force of P = 580 lb, an internal shear force of V = 420 lb, and an internal bending moment of M = 6,400 lb·in., acting in the directions shown in Figure P12.5a. The cross-sectional dimensions (Figure P12.5b) of the extrusion are b1 = 2.0 in., t1 = 0.6 in., b 2 = 4.0 in., t2 = 0.4 in., d = 4.5 in., and tw = 0.4 in. Determine the normal and shear stresses acting on horizontal and vertical planes: (a) at point H, which is located at a distance of yH = 0.8 in. above the z centroidal axis. (b) at point K, which is located at a distance of yK = 1.1 in. below the z centroidal axis. Show the stresses on a stress element for each point.