WORLD FOR CIVIL

Topic 3.83: Thermal Stress, Strain, & Deformation - Problems

The following values will be need for the Problems below
Linear coefficient of Expansion:
_Steel = 6.5 x 10^-6/^oF; _Aluminum = 13 x 10^-6/^oF ; _Brass = 11 x 10^-6/^oF; _concrete = 6 x 10^-6/^oF
Young's Modulus:
E_Steel = 30 x 10⁶ lb/in²; E_Aluminum = 10 x 10⁶ lb/in²; E_Brass = 15 x 10⁶ lb/in²; E_Concrete = 5 x 10⁶ lb/in²

1. A concrete sidewalk slab is 3 ft. wide by 4 ft. long. If the concrete slab is constrained so it can not expand, what stress would develop in it due to thermal effects if it experienced a temperature increase of 60^o F? (Stress = 1800 psi.)

2. An aluminum rod and a brass rod are attached to each other, and the aluminum rod is attached to a wall as shown in the diagram. The rods are initially unstressed and then a 20, 000 lb horizontal force is applied to the end of the brass rod as shown. Additionally, the rods experience a temperature increase of 80 ^o F. Determine the final stress that develops in each rod, and the total movement of point C. (Al. stress = 10,000 psi.; Br. stress = 20,000 psi.; Total def. = .384")

3. A steel rod and a brass rod are attached to each other and mounted between two walls as shown in the diagram. If the structure is initially unstressed and then experiences a temperature increase of 80^o F., determine the stress which develops both in the steel and in the brass rod, and the amount of deformation of the brass rod. ( St. stress = 8000 psi.; Br. stress = 16000 psi.; Def. of Br.=.0182")

4. A horizontal bar ABDF is pinned to the wall at point A, and supported by steel member BC and aluminum member DE, as shown in the diagram. If the structure is initially unstressed and then experiences a temperature decrease of 70^o F., determine the stress which develops in the steel and aluminum members, and the movement of point F.(St.stress =9444 psi.; Al stress = 2951 psi.; Move. of F = -.074")

5. In the structure shown below horizontal member BCD is supported by vertical brass member, AB, an aluminum member DE, and by a roller at point C. Both AB and ED have cross sectional areas of .5 in². If the structure is initially unstressed and then experiences a temperature increase of 90 degrees, determine the stress that develops in aluminum member DE, and the movement of Point B. (Al. stress = 5470 psi.; Move B.= -.01")