MAE 101: Homework 3 Solution
October 13, 2011
Problem 6.8
The Howe and Pratt bridge trusses are subjected to identical loads.
1. In which truss does the largest tensile force occur?
In what member(s) does it occur, and
what is its value?
2. In which truss does the largest compressive force occur? In what member(s) does it occur,
and what is its value?
B
C
D
L
F
F
F
E
A
Howe
G
H
I
L
L
L
L
Solution:
(a)
Howe Bridge:
The moment about
A
is
M
A
=

6
F
+ 4
E
= 0, from which
E
=
3
2
F
. Denote
the axial force in the member
I
,
K
by
IK
.
(1)
Joint E
:
DE
=

E
sin 45
◦
=

3
√
2
2
F
(
C
)
EI
=
DE
cos 45
◦
=
3
2
F
(
T
)
(2)
Joint D
:
CD
=
DE
cos 45
◦
=

3
2
F
(
C
),
DI
=

DE
sin 45
◦
=
3
2
F
(
T
)
(3)
Joint I
:
CI
=
F

DI

sin 45
◦
=

√
2
2
F
(
C
),
HI
=
EI

CI
sin 45
◦
= 2
F
(
T
)
(4)
Joint H
:
CH
=
F
(
T
)
, GH
=
HI
= 2
F
(
T
).
By symmetry (the reaction at
A
has no
x
component) the axial forces in the other members are
HG
=
HI
,
CG
=
CI
,
BG
=
DI
,
CD
=
BC
,
AG
=
EI
, and
AB
=
DE
.
In the Howe truss, the members
HI
and
GH
have the highest tensile force
GH
=
HI
= 2
F
(
T
)
and the members
DE
and
AB
have the highest compressive
force
AB
=
DE
=

3
√
2
2
F
(
C
)
(b)
Pratt Bridge:
The moment about
A
is
M
A
=

6
F
+ 4
E
= 0, from which
E
=
3
2
F
.
1
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L
F
F
E
A
Pratt
B
C
D
G
H
I
F
L
L
L
L
F
E
F
A
B
C
D
L
F
F
F
E
A
B
C
D
G
H
G
H
I
F
L
L
L
L
L
L
L
L
L
I
A
X
A
Y
F
DE
CD
DE
DI
EI
E
F
F
E
L
L
L
L
L
45
°
45
°
45
°
45
°
45
°
45
°
45
°
45
°
HI
CI
DI
EI
F
GH
HI
CH
F
(1) Joint
E
(2) Joint
D
(5) Joint
H
(3) Joint
I
(4) Joint
H
(1) Joint
E
(2) Joint
I
(3) Joint
D
(4) Joint
C
EI
DE
E
F
DI
EI
HI
DC
DH
DI
DE
BC
DC
CH
F
BH
HI
GH
Howe Bridge
Pratt Bridge
(1)
Joint E:
DE
=

3
√
2
2
F
(
C
),
EI
=

DE
√
2
=
3
2
F
(
T
)
(2)
Joint I
:
DI
=
F
(
T
),
HI
=
EI
=
3
2
F
(
T
)
(3)
Joint D
:
DH
=

√
2
DI

DE
=
√
2
2
F
(
T
),
DC
=
DE
√
2

DH
√
2
=

2
F
(
C
)
(4)
Joint C
:
BC
=
DC
=

2
F
(
C
),
CH
= 0
(5)
Joint H
:
GH
=
HI
=
3
2
F
(
T
). The axial forces in the remaining members are determined from symmetry.
In the Pratt Bridge, the highest tensile force occurs in members
EI
,
HI
,
GH
, and
AG
=
3
2
F
(
T
)
, and the highest
compressive force occurs in members
DE
and
AB
=

3
√
2
2
F
(
C
)
. Thus (a) the Howe bridge has the highest tensile
force in a member, and (b) the value of the compressive force is the same in members
DE
and
AB
=
3
√
2
2
F
(
C
) for
both bridges.
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 Spring '08
 ORIENT
 Statics, Force, Trigraph, ax, LTBC Howe

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