A 15.39 short rectangular post supports compressive loads of P = 175 kN and Q = 90 kN as shown in
Fig. P15.39a. A top view of the post showing the locations where loads P and Q are applied to the top of
the post is shown in Fig. P15.39b. Determine the vertical normal stresses at corners a, b, c, and d of the
post.
Fig. P15.39a
Fig. P15.39b Top view of post
Solution
Section properties:
A = (120 mm)(160 mm) = 19, 200 mm 2
(120 mm)(160 mm)3
= 40.960 106 mm 4
12
(160 mm)(120 mm)3
Iz =
= 23.040 106 mm 4
12
Ix =
Equivalent forces at base of post:
F = 175 kN + 90 kN = 265 kN = 265,000 N
M x = (175 kN)(60 mm) (90 kN)(40 mm) = 6,900 kN-mm = 6.900 106 N-mm
M z = (175 kN)(40 mm) = 7,000 kN-mm = 7.000 106 N-mm
Axial stress due to F:
265,000 N
axial =
= 13.802 MPa (C)
19, 200 mm 2
Bending stress due to Mx:
M x z (6.900 106 N-mm)( 80 mm)
bend x =
=
= 13.477 MPa
Ix
40.960 106 mm 4
Bending stress due to Mz:
M z x (7.000 106 N-mm)( 60 mm)
bend z =
=
= 18.229 MPa
Iz
23.040 106 mm 4
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Normal stresses at corners a, b, c, and d: The normal stresses acting at each of the four corners of the
post can be determined by superimposing the results obtained above. In all instances, the normal stresses
act in the vertical direction; that is, the y direction. The sense of the stress, either tension or compression,
can be determined by inspection.
Corner a:
a = 13.802 MPa (C) + 13.477 MPa (T) + 18.229 MPa (C)
= 13.802 MPa + 13.477 MPa 18.229 MPa
= 18.555 MPa = 18.56 MPa (C)
Ans.
Corner b:
b = 13.802 MPa (C) + 13.477 MPa (T) + 18.229 MPa (T)
= 13.802 MPa + 13.477 MPa + 18.229 MPa
= 17.904 MPa = 17.90 MPa (T)
Ans.
Corner c:
c = 13.802 MPa (C) + 13.477 MPa (C) + 18.229 MPa (T)
= 13.802 MPa 13.477 MPa + 18.229 MPa
= 9.049 MPa = 9.05 MPa (C)
Ans.
Corner d:
d = 13.802 MPa (C) + 13.477 MPa (C) + 18.229 MPa (C)
= 13.802 MPa 13.477 MPa 18.229 MPa
= 45.508 MPa = 45.5 MPa (C)
Ans.
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.