sm7 20

________________________________________________________________________
PROBLEM (7.20) A simple beam AB with a T-cross section carries a concentrated load P as
shown in Fig. P7.20. Determine the maximum tensile stress t
σ
and largest compressive stress c
σ
in the
member.
Given: P = 6 kN, L = 3 m, a = 1 m, b = 75 mm, b1 = 25 mm, h = 100 mm, h1 = 75 mm
SOLUTION
ii
i
Ay
yA =∑
∑
(75 25)(12.5) (75 25)(62.5)
(75 25) (75 25)
×+×
=×+× 37.5 mm
=
y
and and
137.5cm=m262.5cmm
=
32
1(75)(25) (75 25)(25)
12
z
I=+×
32
1(25)(75) (75 25)(25)
12
++ ×
=
64
3.32(10 ) mm
max 6(1)
() (31)4
3
Pa
M
La kNm
L
=−= −=⋅
3
max 1 6
(4 10 )(0.0375) 45.18
3.32(10 )
tz
Mc
M
Pa
I
σ
−
×
== =
3
max 2 6
(4 10 )(0.0625) 75.3
3.32(10 )
cz
Mc
M
Pa
I
σ
−
×
==− =−
z
y
25
75
c1
C100
c2
A
2
A
175
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