4.99 Knowing that the magnitude of the vertical force P is 2 kN, deter- mine the stress at (a) point A, (b) point B. IP A TD B 18 mm 40 mm 12 mm 12 mm Fig. P4.99

Problem 4.1

A roadway sign weighs 5.3 kN and is supported by a structural pipe that has an outside diameter of 220 mm and a wall thickness of 14.5 mm. The resultant force of the wind pressure acting on the sign is 13 kN, as shown. Assume a = 8.1 m, b=4m, P₂ = 13 kN, and Py = 5.3 kN. (a) Determine the normal and shear stresses. Txy at point H. (b) Determine the normal and shear stresses Ok Tysk at point K. Answers: 0|| = Tryll = 0k = Tyck= i i MPa. MPa. MPa. MPa.

The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm is subjected to the stresses ox, Oy and txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx'y+Cxy, with A=B=C =1 (a) Determine the values of stresses (ox, Oy and txy) at point (x_y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plate that are consistent with o (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). 112 mm 4 m 6 m Fig. 1 Biharmonic Equation ô*o(x, y) ôx o*o(x.y) ô*¢(X.y)=v*o(x,y) =0 +2 where o(x.y) is defined as: ô*o(x,y) o o(x, y) ôxcy