[SOLVED] MECH 260-202 Midterm 2 2023W2

MECH 260-202: Midterm 2 (2023W2)

Questions

1. (18 points) In the system below, discs B and D have a high-friction surfaces and do not slip relative to one another.

If the applied torque Tp is 12N-m, what are the torsional reaction torques at A and C?

2. (7 points) Beam ABCD is supported by a pin joint at A and a roller joint at D. The magnitude of the distributed load between C and D begins at 1N/m at C and decreases linearly to ON/m at D. Draw a shear and bending moment diagram for the beam and mark the z location at which the maximum bending stress occurs (you do not need to calculate the exact value of z or the magnitude of the maximum bending moment).

3. A long slender beam is subjected to a varying bending moment as illustrated below:

The beam is made of steel with Estcel=29000 ksi and has a W36x300 profile, which

• is horizontally and vertically symmetrical,
• has cross-sectional area A = 88.3in2 and height h = 36.74 in, and
• has second rectangular moments of area I=20300in and I,= 1110 in4.

Given this information:

(a) (4 points) Find most tensile and most compressive bending stress experienced anywhere in the beam.

(b) (2 points) Mark the location (s) where the most tensile and most compressive bending stress appears in the "Side View" section of the diagram above or your own neat sketch. Be sure to label which is which.

(c) (6 points) The beam is reinforced by adding a layer of aluminum with EAi = 10600ksi to its top surface. The final geometry is:

Sketch one possible transformed cross-section which is relevant to analyzing the bending stresses which develop in the reinforced beam under the same loading M(z). Locate its the relevant neutral axis and evaluate the relevant second moment of area. Note: the flange and web thicknesses of the W36x300 profile are deliberately not provided.