ENGN.2060 Lecture Notes - Lecture 5: Horse Length
13 Jun 2018
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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.
128
4.5 ft
18 in.
P
PROBLEM 2.35
The 4.5-ft concrete post is reinforced with six steel bars, each with a 1
8
1-in. diameter.
Knowing that Es 29 × 106 psi and Ec = 4.2 × 106 psi, determine the normal stresses
in the steel and in the concrete when a 350-kip axial centric force P is applied to the
post.
SOLUTION
Let portion of axial force carried by concrete.
portion carried by the six steel rods.
c
s
P
P
()
ccc
c
cc
sss
s
ss
cs cc ss
cc ss
PL E A
P
EA L
PL E A
P
EA L
PP P EA EA
L
P
LEAEA
G
G
G
G
G
G
H
222
222
2
3
4
6262
6
6(1.125in.)5.9641in
44
(18 in.) 5.9641 in
44
248.51 in
4.5 ft 54 in.
350 10 lb 2.8767 10
(4.2 10 psi)(248.51 in ) (29 10 psi)(5.9641in )
u
u
uu
ss
ccs
Ad
AdA
L
SS
SS
H
64
(29 10 psi)( 2.8767 10 ) 8.3424 10 psi
ss
E
VH
u u u
V
s
8.34 ksi W
643
(4.2 10 psi)( 2.8767 10 ) 1.20821 10 psi
u u u
cc
E
VH
V
c 1.208 ksi W
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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.
132
B
C
15 in.
25 in. 1.25 in.
A
6 kips
6 kips
2 in.
PROBLEM 2.39
A polystyrene rod consisting of two cylindrical portions AB and BC is restrained at
both ends and supports two 6-kip loads as shown. Knowing that 6
0.45 10 psi, u
E
determine (a) the reactions at A and C, (b) the normal stress in each portion of
the rod.
SOLUTION
(a) We express that the elongation of the rod is zero.
22
44
0
BC BC
AB AB
AB BC
PL
PL
dE dE
SS
G
But
A
BA BCC
P
RPR
Substituting and simplifying,
22
0
CBC
AAB
AB BC
RL
RL
dd
22
25 2
15 1.25
§· §·
¨¸ ¨¸
©¹
©¹
BC
AB
CAA
BC AB
d
L
R
RR
Ld
4.2667
CA
R
R (1)
From the free body diagram, 12 kips
AC
RR (2)
Substituting (1) into (2), 5.266712
A
R
2.2785 kips
A
R 2.28 kips
A
R n W
From (1), 4.2667(2.2785)9.7217 kips
C
R
9.72 kips
C
R n W
(b) 2
4
2.2785
(1.25)
S
V
AB A
AB
AB AB
PR
AA 1.857 ksi
AB
V
W
2
4
9.7217
(2)
BC C
BC
BC BC
PR
AA
S
V
3.09 ksi
BC
V
W
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Document Summary
The 4. 5-ft concrete post is reinforced with six steel bars, each with a. Knowing that es (cid:32) 29 106 psi and ec = 4. 2 106 psi, determine the normal stresses in the steel and in the concrete when a 350-kip axial centric force p is applied to the post. P s (cid:32) (cid:32) portion of axial force carried by concrete. portion carried by the six steel rods. (cid:71) (cid:32) (cid:71) (cid:32) 54 in. (cid:117) (cid:14) (4. 2 10 psi)(248. 51 in ) (cid:16) 6 (4. 2 10 psi)( 2. 8767 10 ) 1. 20821 10 psi (cid:117) (cid:16) 3 (cid:117) (cid:117) (cid:86)s (cid:32) (cid:16)8. 34 ksi (cid:87)(cid:3) (cid:86)c (cid:32) (cid:16)1. 208 ksi (cid:87)(cid:3) A polystyrene rod consisting of two cylindrical portions ab and bc is restrained at both ends and supports two 6-kip loads as shown. 0. 45 10 psi, determine (a) the reactions at a and c, (b) the normal stress in each portion of the rod. (cid:117) (cid:32)
