1. Find the reaction at support A for the beam shown below.
2. What is the vertical coordinate of the centroid (yc) for the section shown below? All dimensions are in inches. Use the datum (y = 0) as indicated. Do not choose your own datum.
3. What is most nearly the centroidal moment of inertia (Ix) of the section shown below? All dimensions are in inches.
4. What is the elongation of a rectangular bar (cross section 2 inch x 2 inch, length 4 ft) when it is subjected to an axial load of 80,000 lbs. Assume the material of the bar has the following properties: G = 7,700 ksi, v = 0.30
5. A beam is loaded as shown below. What is the bending moment function in the domain 4 < x < 10? The reaction on the right support (B) has been calculated as 36.4 kips (upward).
6. Draw a qualitative shape for the bending moment diagram for the beam loaded as shown. Clearly state any assumptions you make.
7. The stress state at a point within a structure is as shown below. All stresses are in MPa. What is the normal stress on a plane inclined at 35 degrees to the horizontal? Shear stress components are shown as dashed lines.
8. A T-shaped section (see below) has the following properties: cross sectional area = 3000 mm2, distance to neutral axis (centroid) yc = 74 mm, overall depth d = 125 mm, moment of inertia I = 1.65x107mm 4. The section is subjected to a positive bending moment M = 40 kNm as shown. What is the maximum bending stress? Indicate tension or compression.
9. A simply supported beam (see figure below) supports a uniformly distributed load w = 6 kip/ft.
The beam has an I-shaped section as shown below (All dimensions are inches)
What is the maximum shear stress?
10. A hollow tube is subjected to a torque of 4 kNm. Assume that the tube can be classified as a THIN-WALLED TUBE. The cross section of the tube is shown below. Use G = 80 GPa
What is the twist angle if the length of the shaft is 60 cm long?
11. A steel (E = 200 GPa, α = 10 x 10-6 /o C) rod of diameter 2 cm is welded to fixed supports as shown. The temperature is raised by 100o C. What is the stress is the rod?
12. A hollow circular cylinder made of steel (E = 200 GPa, G = 77 GPa) is subject to a torque T at one end and is fixed at the other end. Outer diameter of the rod is 50 mm and inner diameter is 44 mm. The length of the rod is 60 cm. What is the maximum torque so that the allowable shear stress (300 MPa) is not exceeded and the twist angle does not exceed 3 degrees?