Most materials expand when heated and contract when cooled. In many materials, t

Question

Most materials expand when heated and contract when cooled. In many materials, this effect can be described by the relation Delta l/l_0 = alpha_L(T - T_0) where alpha_L is the linear thermal expansion coefficient. If the ends of the part are constrained to prevent them from moving, a temperature change creates thermal stress in the material: sigma_th = E alpha_L(T - T_0) A brass rod is to be used in an application requiring its ends to be held rigid. If the rod is stress-free at room temperature [20 degree C (68degree F)], what is the maximum temperature to which the rod may be heated without exceeding the compressive stress of 172 MPa (25000 psi)? Assume a modulus of elasticity of 100 GPa (14.6 times 10^6 psi) and a linear thermal expansion coefficient of 20.0 times 10^-6 K for brass. (Callister and Rethwisch, 2016)

Explanation / Answer

thermal stress = Y*strain

thermal stress = 172 MPa
thermal stress = 172*106 Pa
Y = 100 GPa
Y = 1011 Pa
T1=20 C
=(273+20)K
=293 K
strain = cofficient of thermal expansion *(T2-T1)
strain = 20*10-6 *(T2-293)

now use
thermal stress = Y*strain
172*106 =1011 *20*10-6 (T2-293)
(T2-293) = 86 K
T2 = 379 K

ANSWER: 379 K

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.