18 ft q = 300 lb/ft | 400 lb/ft B A F10 ft -10 ft→- 6 ft→f-6 ft→ PROBLEM 4.3-5

A pole is fixed at the base and is subjected to a linearly varying distributed force with maximum intensity of q and an axial compressive load P = 29 kips at the top (see figure). d₁ 10 ft 90=400 lb/ft The pole has a circular cross section with an outer diameter of 6.0 in. and an inner diameter of 5.5 in. Find the normal stresses on the surface of the pole at the base at locations A and B. (Assume that the bending moment is not affected by the presence of lateral deflections. Enter your answers in ksi. Use the statics sign convention. Assume that the +x-axis is to the right.) σ, ksi OF ksi d₂

Prob.2 Determine (a) the maximum bending stress, (b) the maximum shearing stress due to V in the simply supported beam shown in the figure and (c) the shearing stress at a point 1m from the right support and 2 cm below the top. 40 kN/m 5 сm 16 kN m 16 cm - 1m- - 2 m - 2 m-

A cantilever beam of rectangular cross section is subjected to a concentrated load P = 150 kN acting at the free end (see Figure 1). The beam has width b = 80 mm. and height h = 260 mm. Point A is located at distance c = 0.5 m from the free end and distance d = 220 mm. from the bottom of the beam. a) Using Mohr's circle, calculate the principal stresses oơi and oz and the maximum shear stress Tmax at point A. b) Show these stresses on sketches of properly oriented elements. P b. Figure 1: A cantilever beam

H.W.1 /The cantilever beam in Figure below has a rectangular cross section with dimension (20 mm(width) x40 mm (height)).(a). Find the maximum bending stress (oms) in the beam. (b) Find the maximum bending stress (amar) in point B and C in the beam (c)Sketch the bending stress distribution over the cross scction on which the maximum bending stress occurs. A в 10 Ib/ft C 20 ft 60 ft

Problem 5 Knowing that the ultimate stress at points A, B and D are 30 MPa, 155 MPa and 140 MPa respectively, what is the maximum allowable couple M that can be applied onto the beam of the shown cross section forming an angle B with the vertical plane. B = 15° B M S0 mm 20 mm s0 mm 30 mm

A simply supported beam is subjected to a linearly varying distributed load q(x) = qo with maximum intensity 9, at B. The beam has a length L = 4 m and rectangular cross section with a width of 220 mm and height of 285 mm. %3D 90 9(x) Determine the maximum permissible value for the maximum intensity, go, (in kN/m) if the allowable normal stresses in tension and compression are 130 MPa. kN/m

A simple beam of wide-flange cross section supports a uniform load of intensity q = 45 kN/m on a span of length L = 3 m. The dimensions of the cross section are h = 270 mm, b = 180 mm, and tf = 15 mm, tw = 12 mm, d = 0.8 m, and a = 60 mm. (a) Calculate the maximum shear stress omax on cross section A-A located at distance d = 0.6 m from the end of the beam. (b) Calculate the shear stress oB at point B on the cross section. Point B is located at a distance a = 60 mm from the edge of the lower flange. 2 2 A+ h 2 В

The overhanging beam ABC in Figure supports a concentrated load and a uniformly distributed load. The beam has a rectangle cross-sectional area of 120 mm × 180 mm (base x height). Neglect the weight of the beam. a) Construct the shear-force and bending-moment diagram. b) Determine the maximum normal stress in the beam and its location measured from point A. Ans : omax 173.92 MPa 20 kN 12 kN/m A B 4 m 10 m 20

The cantilever beam is subjected to a concentrated load P. The cross-sectional dimensions of the rectangular tube shape are shown in the second figure. Assume b = 133 mm, d = 207 mm, y = 62 mm, yk = 37 mm and t = 6 mm. (a) Compute the value of Q that is associated with point H, which is located 62 mm above the centroid of the rectangular tube shape. (b) If the allowable shear stress for the rectangular tube shape is 117 MPa, determine the maximum concentrated load P that can be applied to the cantilever beam. Answers: (a) Q = (b) P = i i P Z mm³. kN. ун Ук H K b t (typ.)