ENGN.2060 Lecture Notes - Lecture 6: Ferrari 250, Thermal Expansion
13 Jun 2018
School
Department
Course
Professor
PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use.
Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted
on a website, in whole or part.
148
6 ft
10 in.
10 in.
PROBLEM 2.50
The concrete post 6
(3.610
c
E u psi and 6
5.5 10 / F)
D
uq
c is reinforced with six steel
bars, each of 7
8-in. diameter 6
(2910
s
E u psi and 6
6.5 10 / F)
.
D
uq
s
Determine the
normal stresses induced in the steel and in the concrete by a temperature rise of 65°F.
SOLUTION
2
22
7
66 3.6079 in
448
SS
§·
¨¸
©¹
s
Ad
22 2
10 10 3.6079 96.392 in
cs
AA
Let c
P
tensile force developed in the concrete.
For equilibrium with zero total force, the compressive force in the six steel rods equals .
c
P
Strains: () ()
cc
sscc
ss cc
PP
TT
EA EA
HDHD
' '
Matching: cs
H
H
() ()
cc
cs
cc ss
PP
TT
EA EA
DD
' '
6
66
3
11 ()()
11
(1.0 10 )( 65)
(3.6 10 )(96.392) (29 10 )(3.6079)
5.2254 10 lb
DD
§·
'
¨¸
©¹
ªº
u
«»
uu
¬¼
u
csc
cc ss
c
c
PT
EA EA
P
P
3
5.2254 10 54.210 psi
96.392
c
c
c
P
A
V
u
54.2 psi
c
V
3
5.2254 10 1448.32 psi
3.6079
c
s
s
P
A
V
u
1.448 ksi
s
V
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The concrete post bars, each of 7 normal stresses induced in the steel and in the concrete by a temperature rise of 65 f. is reinforced with six steel (cid:117) P (cid:32) tensile force developed in the concrete. c. For equilibrium with zero total force, the compressive force in the six steel rods equals. E a c c (cid:14) (cid:68) c (cid:39) E a s s (cid:14) (cid:68) s (cid:39) P c (cid:32) (cid:183) (cid:184) (cid:185) (cid:68) (cid:68) (cid:16) c s (cid:39) 6 (cid:117) (3. 6 10 )(96. 392) (29 10 )(3. 6079) (cid:14) P c (cid:32) (cid:186) (cid:187) (cid:188) (1. 0 10 )(65) (cid:117) (cid:16) A rod consisting of two cylindrical portions ab and bc is restrained at both (cid:113) ends. Portion ab is made of steel ( and portion bc is made of brass ( Knowing that the rod is initially unstressed, determine the compressive force induced in. Abc when there is a temperature rise of 50 c. (cid:113) (cid:32)
