sm7 141 142

________________________________________________________________________
PROBLEMS (7.141 and *7.142) A singly symmetric steel beam has the cross section shown in
Figs. 7.141 and 142. (Dimensions are in millimeters.) Calculate the plastic moment Mp .
Assumption: The steel is to be elastoplastic with a yield stress of y
σ
= 250 MPa.
SOLUTION (7.141)
2
2(10)(40) (10)(30) 1100Am=+=m
Neutral axis divides section into two equal areas:
2
1
(30) (10) 2(10)( ) 550
2
A
hm+==
mh mm==
y
m
10
Solving
hm
12
12.5 27.5
Therefore,
12
()
2
Ay y
Z
+
=
where
2
1
111
1[2( )(10)( ) 10(30)( 5) ] 6.93
22
ii
i
Ay h
y
hh
AA
== + −=
∑
∑mm
2
22
1[2(10)( )( )] 13.75
22
h
y
hm
A
==m
So
3
1100 (6.93 13.75) 11,374
2
Z
mm=+=
σ
−
==× ×
MZ
66
(250 10 )(11,374 10 )
py
=⋅
2.84 kN m
SOLUTION (*7.142)
(125)(10) (200)(10) (250)(10)A=++
32
5.75 10 mm=×
Neutral axis divides section into two equal areas:
3
1
( 250)(10) ( 10)(10) 2.875 10
2
A
h+− == ×
mh mm==
Solving
hm
12
47.5 172.5
Hence
y
125 mm
z
10 mm
10 mm
250 10 mm
200 m
m
h
1
h2
z
10 10
h
1
30
h2
30
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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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Continued on next slide

12
()
2
Ay y
Z+
=
where
2
111
11
[(250)(10)( 5) (10)( 10) ( )] 39.402
22
ii
i
Ay
y
hh
AA
== −+− =
∑
∑mm
2
222
11
[(125)(10)( 5) 10( 10) ( )] 118.75
22
y
hh
A
=−+−=mm
Thus
33
5750 (39.402 118.75) 454.687(10 )
2
Z
mm=+=
66
(250 10 )(454.687 10 ) 113.7
py
M
ZkNm σ
−
=× × = ⋅
=
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.