Questions from Mechanics

Q: The frame shown in the figure consists of a beam ACB supported

The frame shown in the figure consists of a beam ACB supported by a strut CD. The beam has length 2L and is continuous through joint C. A concentrated load P acts at the free end B. Determine the vert...

Q: The cantilever beam ACB shown in the figure supports a uniform load

The cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its length. The beam has moments of inertia I2 and I1 in parts AC and CB, respectively. (a) Using the meth...

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 th...

Q: A simple beam AB of length L and height h (see

A simple beam AB of length L and height h (see figure) is heated in such a manner that the temperature difference T2 – T1 between the bottom and top of the beam is proportional to th...

Q: A simple beam ABCD has moment of inertia I near the supports

A simple beam ABCD has moment of inertia I near the supports and moment of inertia 2I in the middle region, as shown in the figure. A uniform load of intensity q acts over the entire length of the bea...

Q: A beam ABC has a rigid segment from A to B and

A beam ABC has a rigid segment from A to B and a flexible segment with moment of inertia I from B to C (see figure). A concentrated load P acts at point B. Determine the angle of rotation Î&cedi...

Q: A simple beam ABC has a moment of inertia 1.5I

A simple beam ABC has a moment of inertia 1.5I from A to B and I from B to C (see figure). A concentrated load P acts at point B. Obtain the equations of the deflection curves for both parts of the be...

Q: A tapered cantilever beam AB supports a concentrated load P at the

A tapered cantilever beam AB supports a concentrated load P at the free end (see figure). The cross sections of the beam are rectangular tubes with constant width b, outer tube depth dA at A, and oute...

Q: Repeat Problem 10, but now use the tapered propped cantilever tube

Repeat Problem 10, but now use the tapered propped cantilever tube AB with sliding support at B (see figure) that supports a concentrated load P at the sliding end. Find the equation of the deflection...

Q: The load on a cantilever beam AB has a triangular distribution with

The load on a cantilever beam AB has a triangular distribution with maximum intensity qo (see figure). Determine the angle of rotation θB and the deflection dB at the free end.