For the cantilever steel beam [E = 220 GPa; I = 86 x 10 mm ], use the double-integration method to determine the deflection VA at A. Assume L = 2.5 m, P = 59 kN, and w = 21 kN/m. Answer: VA = mm.
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![For the cantilever steel beam [E = 220 GPa; I = 86 x 106 mm*], use the double-integration method to determine the deflection VA at A.
Assume L = 2.5 m, P = 59 kN, and w = 21 kN/m.
Answer: VA =
mm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82629b11-ea44-412f-b7ab-370838a64f0a%2F2352897e-60ea-4857-b094-f95b3acf5d8c%2Fu4ttuki_processed.jpeg&w=3840&q=75)
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- Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.Solve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa.Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses Jt(and k2^ and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the moment MQis applied? Data for the structure are M0 = 7.5 kip-ft, L = 6 ft, EI = 520 kip-ft2, kx= 17 kip/ft, and As = 11 kip/ft. Repeat part (a), but remove Af0 and instead apply uniform load q over the entire beam.
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- 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.)Beam AB has an elastic support kR at A, pin support at B, length L, height h (see figure), and is heated in such a manner that the temperature difference T2T1 between the bottom and top of the beam is proportional to the distance from support A. Assume the temperature difference varies linearly along the beam: T2T1=T0x in which T0 is a constant having units of temperature (degrees) per unit distance. Assume the spring at A is unaffected by the temperature change. Determine the maximum deflection max of the beam, Repeat for a quadratic temperature variation along the beam, so T2T1=T0x2 What is max for parts (a) and (b) if kR goes to infinity?A beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the free end C (see figure). Determine the strain energy Ustored in the beam due to the load P. From the strain energy, find the deflection Scunder the load P. Calculate the numerical values of £/and Sc if the length L is 8 ft, the overhang length a is 3 ft, the beam is a W 10 x 12 steel wide-flange section, and the load P produces a maximum stress of 12,000 psi in the beam, (Use £ = 29 X 106 psi.)
- Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint B so that the total deflection at joint B is zero. Assume that£ = 16,000 ksi.Solve the preceding problem using the following data: beam cross section is 100 x 150 mm, length is 3 m, and point load is P = 5 kN at mid-span, Point C is located 25 mm below the top of the beam and 0.5 m to the right of support A.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.