This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Sec_2.5.qxd 9/25/08 3:00 PM Page 161 161 SECTION 2.5 Thermal Effects Misfits and Prestrains
Problem 2.5-12 A steel wire AB is stretched between rigid supports (see
figure). The initial prestress in the wire is 42 MPa when the temperature is 20°C.
(a) What is the stress in the wire when the temperature drops to 0°C?
(b) At what temperature T will the stress in the wire become zero?
14 10 6/°C and E 200 GPa.)
(Assume Solution 2.5-12 Steel wire with initial prestress
From Eq. (2-18):
1 Initial prestress: 1 Initial temperature: T1
E 42 MPa (200 GPa)(14 20°C 42 MPa 56 MPa 1 T2 0°C 10 6/°C)(20°C)
; 98 MPa (b) TEMPERATURE WHEN STRESS EQUALS ZERO 10 6/°C (a) STRESS E ( T) 1 42 MPa 200 GPa
14 2 E ( T) 2 WHEN TEMPERATURE DROPS TO T 0°C 20°C 2 0 1 E ( T) 0 s1
Ea ¢T NOTE: Positive T means a decrease in temperature
and an increase in the stress in the wire. (Negative means increase in temp.) Negative T means an increase in temperature and a
decrease in the stress. ¢T Stress
stress equals the initial stress 1 plus the additional
2 due to the temperature drop. T 42 MPa 15°C (200 GPa)(14 * 10 6/°C
20°C 15°C 35°C
; 0.008 in. Problem 2.5-13 A copper bar AB of length 25 in. and diameter 2 in. is placed in position at A room temperature with a gap of 0.008 in. between end A and a rigid restraint (see figure). The
bar is supported at end B by an elastic spring with spring constant k 1.2 106 lb/in.
(a) Calculate the axial compressive stress c in the bar if the temperature
9.6 10 6/°F and E 16 106 psi.)
rises 50°F. (For copper, use
(b) What is the force in the spring? (Neglect gravity effects.)
(C) Repeat (a) if k : 25 in. d = 2 in.
k C ...
View Full Document