The beam given in the figure below is subjected to the uniform distributed load of w=50 kN/m. (a) Draw shear diagram (b) Determine the maximum shear stress in the beam: A B- 3 m- 3 m 50 mm 100 mm
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- A hollow steel box beam has the rectangular cross section shown in the figure. Determine the maximum allowable shear force K that may act on the beam if the allowable shear stress is 36 MPa. cA wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C. The loads consist of a horizontal force P1= 4,0 kN acting at the end of a vertical arm and a vertical force P2= 8.0 kN acting at the end of the overhang, Determine the shear force Fand bending moment M at a cross section located 3,0 m from the left-hand support. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations, Find the value of load A that results in V = 0 at a cross section located 2.0 m from the left-hand support. If P2= 8.0 kN, find the value of load P1that results in M = 0 at a cross section located 2,0 m from the left-hand support.
- The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are b = 6.54 in., h = 8.06 in., fw = 0.285 in., and tf = 0.465 in.. The loads on the beam produce a shear force V = 7.5 kips at the cross section under consideration. Use center line dimensions to calculate the maximum shear stress raiaxin the web of the beam. Use the more exact analysis of Section 5,10 in Chapter 5 to calculate the maximum shear stress in the web of the beam and compare it with the stress obtained in part .A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.
- The composite beam shown in the figure is simply supported and carries a total uniform load of 40 kN/m on a span length of 4.0 m. The beam is built of a southern pine wood member having cross-sectional dimensions of 150 mm × 250 mm and two brass plates of cross-sectional dimensions 30 mm × 150 mm. Determine the maximum stresses (7b and ctwin the brass and wood, respectively, if the moduli of elasticity are EB= % GPa and Ew= 14 GPa. (Disregard the weight of the beam.) Find the required thickness of the brass plates so that the plate and wood reach their allowable stress values of Eb= 70 MPa and t Ew= 8.5 MPa simultaneously under the maximum moment. What is the maximum moment?A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an outer diameter d1= 100 mm and an inner diameter d2= 94 mm. The plastic liner has an inner diameter d1= 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallowif the allowable stress in the steel is 35 M Pa and in the plastic is 600 kPa. If pipe and liner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (i.e., a balanced design)? What is the new maximum moment?The T-beam shown in the figure has cross-sectional dimensions: b = 210 mm, t = 16 mm, h = 300 mm, and A, = 280 mm. The beam is subjected to a shear force V = 68 kN. Determine the maximum shear stress tntijlin the web of the beam.
- A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are TA= 75 GPa and Es= 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 M Pa in the aluminum, what is the maximum stress xs in the steel? If the height of the beam remains at 120 mm and allowable stresses in steel and aluminum are defined as 94 M Pa and 40 M Pa, respectively, what heights h and h. arc required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure: Also, check the formula for the special case of a channel section (a = 0).