sm9 41

_______________________________________________________________________
PROBLEM (9.41) For a beam loaded as shown in Fig. P9.41, by taking into account the beam's
own weight of 500 N/m, calculate the maximum normal and the maximum shearing stresses at point D
of the cross section at midspan. Show the results on a properly oriented element.
SOLUTION
,
0)5.0(201)2(5.0)2(:0 =−−=
∑BA RM kNRB5.5
=
:0=
∑y
F kNRA5.15=
364
1(80)(160) 27.31 10
12
I
mm==×
mmQ 3 10220555080 ×=××=
36
6
5 10 (220 10 ) 0.504
27.31 10 (0.08)
DVQ
M
Pa
Ib
τ
−
−
××
== =
×
3
6
5.25 10 (0.03) 5.77
27.31 10
DMc
M
Pa
I
σ
−
×
== =
×
22
(2.885) (0.504)R=+ 2.93
M
Pa=
Continued on next slide
D
τ
D
σ
D
15.5
A
B
C
D
-5.5
0.5 kN/m
y
15.25
z
15.5 kN 5.5 kN
-4.75 Vm=5
160
80
1 m
20kN
1.5 m 50
80
0.5 m
V, kN Dimensions
are in
millimeters
x
=
M
m5.5 5
2
+
(1)=5.25
x
M
, kN⋅m
2.885
τ
(MPa)
σ
(psi)
1
σ
(5.77, -0.504)
2θp’
2
R
σ
C
O
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MPa93.2
max =
τ
MPa82.5885.293.2
1=+=
σ
MPa05.0885.293.2
2−=+−=
σ
and 0.504
tan2 ' 2.885
p
θ =
'4.95
p
θ
=
x
4.95o
D
2.93 MPa
0.05 MPa
5.82 MPa
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
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