truss – assumptions
TRANSCRIPT
Truss Truss –– Assumptions Assumptions There are four main assumptions made in the analysis of truss
Truss members are connected together at their ends only.
Truss are connected together by frictionless pins.
The truss structure is loaded only at the joints.
The weights of the members may be neglected.
1
2
3
4
Simple TrussSimple Truss
The basic building block of a truss is a triangle. Large truss are constructed by attaching several triangles together A new triangle can be added truss by adding two members and a joint. A truss constructed in this fashion is known as a simple truss.
Method of Joints Method of Joints --TrussTrussThe truss is made up of single bars, which are either in compression, tension or no-load. Themeans of solving force inside of the truss use equilibrium equations at a joint. This method is known as the method of joints.
Method of Joints Method of Joints --TrussTrussThe method of joints uses the summation of forces at a joint to solve the force in themembers. It does not use the moment equilibrium equation to solve the problem. In a two dimensional set of equations,
In three dimensions,
x y0 0 F F= =∑ ∑
z 0 F =∑
Truss Truss –– Example ProblemExample Problem
Determine the loads in each of the members by using the method of joints.
Truss Truss –– Example ProblemExample Problem
Draw the free-body diagram. The summation of forces and moment about B result in
( ) ( ) ( )
x Ax B
y Ay Ay
A B
B
Ax
0
0 10 kips 10 kips 20 kips
0 5 ft 10 kips 10 ft 10 kips 20 ft60 kips
60 kips
F R R
F R R
M RRR
= = +
= = − − ⇒ =
= = − −
⇒ =⇒ = −
∑∑∑
Truss Truss –– Example ProblemExample Problem
Look at Joint B
x BC B BC BC
y BA BA
0 60 kips 60 kips
0 0 kips
F T R T T
F T T
= = + = + ⇒ = −
= = ⇒ =∑∑
Truss Truss –– Example ProblemExample Problem
Look at Joint D and find the angle
1 o
x DC DA
y DA DA
DC
5 ft.tan 14.0420 ft.
0 cos
0 sin 10 kips 41.231 kips
40 kips
F T T
F T T
T
α
α
α
− = =
= = − −
= = − ⇒ =
= −
∑∑
Truss Truss –– Example ProblemExample Problem
Look at Joint C and find the angle
( ) ( ) ( ) ( )
1 o
y CA CA
x CD CA CB
o
5 ft.tan 26.56510 ft.
0 sin 10 kips 22.361 kips
0 cos
40 kips 22.361 kips cos 26.565 60 kips
0
F T T
F T T T
β
β
β
− = =
= = − ⇒ =
= = − −
= − − − −
=
∑
∑
Example ProblemExample Problem
Determine the forces in members FH, DH,EG and BE in the truss using the method of sections.
Truss Truss –– Example ProblemExample Problem
Draw the free-body diagram. The summation of forces and moment about H result in
( ) ( ) ( ) ( ) ( )
x Hx
Hx
y Hy I
H I
I
Hy
0 3 kips 3 kips 3 kips 3 kips12 kips
0
0 15 ft 3 kips 10 ft 3 kips 20 ft 3 kips 30 ft 3 kips 40 ft20 kips
20 kips
F RR
F R R
M RRR
= = + + + +
⇒ = −
= = +
= = − − − −
⇒ =⇒ = −
∑
∑∑
Truss Truss –– Example ProblemExample Problem
Do a cut between BD and CE
Truss Truss –– Example ProblemExample Problem
Take moment about A
( )( ) ( )
1 0
0A CE
CE
10 fttan 53.137.5 ft
0 cos 53.13 20 ft 3 kips 10 ft
2.5 kips
M T
T
α − = =
= = +
⇒ = −∑
Truss Truss –– Example ProblemExample Problem
Do a cut between HD and GE
Truss Truss –– Example ProblemExample Problem
Take the moment about I
Take the moment about D
( ) ( ) ( )I HD
HD
0 20 kips 15 ft 15 ft 3 kips 10 ft18 kips
M TT
= = − −
⇒ =∑
( ) ( ) ( ) ( )D GE
GE
0 12 kips 20 ft 20 kips 15 ft 3 kips 10 ft 15 ft6 kips
M TT
= = − + + +
⇒ = −∑
Truss Truss –– Example ProblemExample Problem
Do a cut between HD and HI
Truss Truss –– Example ProblemExample Problem
Take the sum of forces in y direction
( )
( )
1 0
0y HF HD
HF 0
10 fttan 53.137.5 ft
0 sin 53.13 20 kips
20 kips 18 kips 2.5 kipssin 53.13
F T T
T
α − = =
= = + −
−⇒ = =
∑