Problem 7.20
Given:
In the figure shown, let b=300 mm, h = 300
mm, t = 25 mm, L = 2.5 m, and P=16.0 kN.
Find: the maximum tensile and compressive stresses
in the beam and the orientation of the neutral axis.
Solution:
A
300mm25
⋅
mm
⋅
275 mm
⋅
25
⋅
mm
⋅
+
14375mm
2
⋅
=
:=
find centroid relative to the bottom edge
y
c
300 mm
⋅
25
⋅
mm
⋅
150
⋅
mm
⋅
275 mm
⋅
25
⋅
mm
⋅
12.5
⋅
mm
⋅
+
A
:=
y
c
84.239 mm
⋅
=
x
c
y
c
:=
relative to right edge
I
x
25 mm
⋅
300 mm
⋅
()
3
12
⋅
300 mm
⋅
25
⋅
mm
⋅
150 mm
⋅
y
c
−
2
⋅
+
275 mm
⋅
25 mm
⋅
3
12
⋅
275 mm
⋅
25
⋅
mm
⋅
y
c
12.5 mm
⋅
−
2
⋅
+
+
...
:=
I
x
1.244
10
8
×
mm
4
⋅
=
I
y
I
x
:=
I
xy
300 mm
⋅
25
⋅
mm
⋅
12.5 mm
⋅
x
c
−
⋅
y
c
150 mm
⋅
−
⋅
275mm25
⋅
mm
⋅
275 mm
⋅
2
25 mm
⋅
+
x
c
−
⎛
⎝
⎞
⎠
⋅
y
c
12.5 mm
⋅
−
⋅
+
...
:=
I
xy
7.398
10
7
×
mm
4
⋅
=
ϕ
90 deg
⋅
:=
cot
ϕ
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This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.
 Spring '10
 MechanicsofSolids
 Stress

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