sm9 45

_______________________________________________________________________
PROBLEM (*9.45) A simply supported beam AB constructed of a W24 x 84 wide-flange section
(refer to Table B.8) is acted upon by three concentrated loads P = 40 kips (Fig. P9.45). Calculate the
maximum principal stress at the junction of a flange and web of the beam.
Assumption: The maximum shear stress is taken as uniformly distributed over the web area and
estimated as avg
τ
= Vmax / d tw by Eq. (7.25).
*SOLUTION
From Table B.8:
4
22370 . 24.10 . 0.47 . 0.77
wf
Iindintint====
V
kips
x
40 ki
p
s
x
M
(kip⋅ft)
2 ft
120 160
2 ft
20
2 ft
2 ft
-60
-20
40 kips 40 ki
p
s
R
A
=60 ki
p
s
60
R
B
=60 ki
p
s
A
B
C
120
D
E
The reactions, as obtained from equations of statics, are indicated on the load
diagram.
At the junction of center C:
max
2
(2 )(160 12)(11.28) 9.138
2370
f
x
Md t ksi
I
σ
−×
== =
max 20 1.766
(24.10)(0.47)
xy avg Vksi
dt
ττ == = =
0
y
σ
=
22
()
2x
x
y
R
σ
τ
=+ 22 (4.569) (1.766) 4.898 ksi=+=
14.569 4.898 9.47
2x
R
ksi
σ
σ =+=+=
Continued on next slide
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.

At junction of point D (or E):
120 40
(9.138) 6.854 (1.766) 3.532
160 20
xxy
ksi ksi στ == ==
22
(3.427) (3.532) 4.921
R
ksi=+=
13.427 4.921 8.35
2x
R
ksi
σ
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.