Questions from Mechanics

Q: A simply supported beam (E = 1 2 GPa) carries

A simply supported beam (E = 1 2 GPa) carries a uniformly distributed load q = 125 N/m, and a point load P = 200 N at mid-span. The beam has a rectangular cross section (b = 75 mm, h = 200 mm) and a l...

Q: An object of weight W is dropped onto the midpoint of a

An object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross section of area A. Assuming that h is very large compared to the d...

Q: Copper beam AB has circular cross section with a radius of 0

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 s...

Q: Beam ABC is loaded by a uniform load q and point load

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 = 2 m, q = 15 kN/m , P = 7.5 kN , E =...

Q: A cantilever beam of a length L = 2.5 ft

A cantilever beam of a length L = 2.5 ft has a rectangular cross section (b = 4 in, h = 8 in) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak inten...

Q: A cantilever beam carries a trapezoidal distributed load (see figure).

A cantilever beam carries a trapezoidal distributed load (see figure). Let wB = 2.5 kN/m, wA = 5.0 kN/m, and L = 2.5 m. The beam has a modulus E = 45 GPa and a rectangular cross section with width b =...

Q: A cantilever beam AB carries three equally spaced concentrated loads, as

A cantilever beam AB carries three equally spaced concentrated loads, as shown in the figure. Obtain formulas for the angle of rotation θB and deflection δB at the free end o...

Q: A simple beam AB supports five equally spaced loads P (see

A simple beam AB supports five equally spaced loads P (see figure). (a) Determine the deflection δ1 at the midpoint of the beam. (b) If the same total load (5P) is distributed as a unifor...

Q: The cantilever beam AB shown in the figure has an extension BCD

The cantilever beam AB shown in the figure has an extension BCD attached to its free end. A force P acts at the end of the extension. (a) Find the ratio a/L so that the vertical deflection of point B...

Q: Beam ACB hangs from two springs, as shown in the figure

Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses k1 and k2 and the beam has flexural rigidity EI. (a) What is the downward displacement of point C, which is at the...