Plastic bar AB of rectangular cross-section (b = 0.75 in. and h = 1.5 in.) and length L = 2 ft is fixed at A and has spring support (k = 18 kips/in.) at C. Initially, the bar and spring have no stress. When the temperature of the bar is raised by 100°F, the compressive stress on an inclined plane p_q at L =1.5 ft becomes 950 psi. Assume the string is massless and unaffected by the temperature change. Let a = 55 X 10^-6 /°F and E = 400 ksi.

(a) What is the shear stress π_θ on plane p_q? What is angle θ?

(b) Draw a stress element oriented to plane pq, and show the stresses acting on all faces of this element.

(c) If the allowable normal stress is +1000 psi and the allowable shear stress is 6560 psi, what is the maximum permissible value of spring constant k if the allowable stress values in the bar are not to be exceeded?

(d) What is the maximum permissible length L of the bar if the allowable stress values in the bar are not be exceeded?

(e) What is the maximum permissible temperature increase (ΔT) in the bar if the allowable stress values in the bar are not to be exceeded?

Transcribed Image Text:

A L=2 ft P Lg=1.5 ft 0 9 B T h