Post on 07-Apr-2018
transcript
8/3/2019 Timoshenko Problem
1/12
A simply supported beam of 2ft. span in subjected to a load of
60,000 lb at its centre the cross-section is show in Fig. Find the
maximum normal and shearing stresses at the junction of theflange and web.
8/3/2019 Timoshenko Problem
2/12
P = 60,000 lb
R2 30,000 lbR1 30,000 lb
1" 1"
+30,000
-30,000
+30,000 lb-ft
+
+
SFD
BMD
8/3/2019 Timoshenko Problem
3/12
C1 = 6"
C2 = 6"
275.05
8/3/2019 Timoshenko Problem
4/12
4
4
13
4
.2
31.286
04.11923.4804.119
)(04.119
23.48023.48
inI
I
symmetrytodueinII
inI AN
43
2
4
2
.1
43
1
23.4812
)5.10)(5.0(
04.1192
75.05)75.5(18.0
18.012
)75.0)(5(
inI
inI
inI
AN
8/3/2019 Timoshenko Problem
5/12
PsiI
MC
f tlbM
lbV
27.754433.286
612000,30
formulebyStressFlexural
000,30
000,30
1max
max
max
Psix
x
x
6601
)75.06(6
20.7544
6
20.7544
75.06
8/3/2019 Timoshenko Problem
6/12
The flexural stress profile is
max -7544.20
(6-0.75)"
6"
-7544.20
x6"
8/3/2019 Timoshenko Problem
7/12
5.6255.25
5.25/2
8/3/2019 Timoshenko Problem
8/12
Psi
bI
VQ
NA
NA
V
17.5871
2
25.525.55.0625.575.05
5.031.286
000,30
formulashearbyStressShear
psi
JunctionAt
xy
4424
2
25.575.05
5.031.286
000,30
8/3/2019 Timoshenko Problem
9/12
4424 Psi
5871.17 Psi
8/3/2019 Timoshenko Problem
10/12
Then the principal stress is
.52.5519
.8820
44242
6601
2
6601
0
22
max
1
2
2
1
2
2
1
Anspsi
Anspsi
As y
xy
yxyx
It is seen that (1) the principal stress at the junction between flange
and web is larger than the tensile stress in the most remote fiber (1 >
max) and therefore should be considered in design.
8/3/2019 Timoshenko Problem
11/12
Find the span length (l) such that the maximum Principal stress
at the junction between flange and the web will be equal to the
maximum flexural stress in the extreme fiber.
I
Pl
I
P
If
VQ
I
Pl
I
Pl
I
Pl
I
Plc
I
MC
xy
x
1.21)5.0(
625.575.3
2
312.112
5.10
)1(5.1
6
44
max
max
8/3/2019 Timoshenko Problem
12/12
.8.39;1580;2.44528.0
5.12.445430.0656.0
(2)and(1)Equating
)2(2.445430.0656.0
0
22
22
22
22
1
2
2
1
inlll
I
Pl
I
Pl
I
Pl
I
Pl
I
Pl
I
Pl
I
Pl
y
xy
yxyx