For the cantilever steel beam [E = 230 GPa; 1= 95 × 106 mm4], use the double-integration method to determine the deflection vg at B. Assume L = 3.5 m, Mo = 67 kN-m, and w = 10 kN/m. A Answer: VB = i W L mm. X Mo
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- A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation B at B results in a reaction moment MB=kRxB. Find rotation B and displacement Bat end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.A cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak intensity qQ= 900 lb/ft. Use the method of superposition and Cases 1 and 9 in Table H-l to calculate the deflection and rotation at B.For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at B, (c) the deflection at the free end, and (d) the slope at the free end. Assume that EI is constant for the beam. Let w = 15 kN/m, L = 3.5 m, E = 185 GPa, and I = 110 x 106 mm4
- For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that EI is constant for the beam. Let w = 12 kN/m, L = 6.0 m, E = 215 GPa, and I = 105 x 106 mm4.a cantilever beam carries uniformlof y distributed load of 800N/m , is 4m long and is supported at te left end by a spring with stiffness equal to 60 kN/m. For the beam E=10GPa and I=80x10^6mm^4. 1. Whic of the following gives the deflection (mm) at the left end when the spring is removed? a. 32 b .30 c. 28 d. 26 2. Which of the following gives the vertical reaction at the left end of the beam? a. 2.55 b.2.60 c. 2.46 d. 2.51 3. Which of the following gives the deflection of the spring in mm? a. 12.31 b. 11.54 c. 10.77 d.10 Answer, 32,12.31,2.46Compute the torsional deflection in degrees of a 110 mm diameter, 1.4 meter long shaft subjected to a twist moment of 3 x 10⁶ N-mm. The torsional modulus of elasticity is 83,000 N/mm². a. 0.27 b. 0.31 c. 0.2 d. 0.24
- a. An overhead line has the following data: Span length= 160 m Conductor diameter= 0.95 cm Weight per unit length of the conductor= 0.65 kg/m Ultimate stress= 4,250 kg/cm2 Wind pressure= 40 kg/m2 Safety factor= 5 Calculate the sag? b. Derive the expression for the lowest point of the catenary curve if the supports are at different levels. Given that weight of conductor= 0.35 kg/m. Maximum allowable tension= 800 kg. Span length= 160 m and safety factor = 2. Find minimum point of catenary if supports are at 70 m and 60 m.For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, and (c) the slope at the free end. Assume that EI is constant for the beam. Let w0 = 6 kN/m, L = 5.5 m, E = 195 GPa, and I = 140 x 106 mm4.a machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original value
- A 70kg human steps at the tip of a springboard used to dive in a pool. The springboard has a length of 1.75 meters, moment of inertia is 0.000002 m^4, and modulus of elasticity is 150 GPa. Determine the deflection of the springboard in millimeters. Note: δ=[(W)(L^3)]/[(3)(E)(I)] for a cantilever beam with end force.Q-2 For the simply supported steel beam [E = 200 GPa; I = 129 × 106 mm4] shownin Figure below, assuming a length L = 6 m, concentrated load of 40 kN, and adistributed load w = 30 kN/m,(a) Use the double-integration method to determine the deflection at B. (b) Use the method of Castigliano to determine the deflection at B.A cantilever of length 2.5 m carries a uniformly distributed load of 16.4 kN per metre length over the entire length. If the moment of intertia of the beam = 7.95 x107 mm4 and value of E = 2 x 105 N/mm2 , Estimate the deflection at the free end.