Question

A sign of dimensions 2.0 m x 1.2 m is supported bt a hollow circular pole having outer diameter 220 mm and inner diameter 180 mm as shown in the figure. The sign is offset 0.5 m from the centerline of the pole and its lower edge is 6.0 m above the ground. The sign is acted by a wind pressure of 2.0 kPa.

a.) determine the normal stress at point A at the base of the pole.

b.) determine the torsional shear stress at point A at the base of the pole.

c.) determine the transverse shear stress at point B at the base of the pole.

0.5 m honeta -2.0 m T Bull's Bookstore 1.2 m 6.0 m B-

Answer 1

T Mr wind pressure aakpa = 2000 N/m2 Total force on sign boord of (2x1.2m) v= 2000 X 1.2x2 4800.0N 116+ 1.3 Resolving this force v to the pole moment -6.6m Mga = VX 6.6 31680N.m ② (Torque) T vx(1.5) 7200 Nom Ilomm gomm Mix y = Ro Outer radius of pole (Ro) = (220mm)/2 inner radius of pole (R;) (180 mm)/ O Normal stress of point A' hey (dit-1.4) (2204-1807); 31680 X 103 54.91 MPa 63460171.6 adlomme moment of inertia) Ia sr 64 69 63460171.6 mm Xllo 2 Torsional Shear stress at point 'A' T = .Ro J= 2*1 = 126920343 mm T 7200X1000 x 110 726920343 = 6.24 MPa 4 ③ Transverse shear stress at point B Tma 52% A TB = {max- 2 V 2x +800 Targ. = (2202-1802) 0.7639 MPa