November 2006
Q1:
A- Define
1- Space truss:
It is a structure consist of members connected together with hinged joints,
- Loads applied at joints not at members
- each joint has three degree of freedom
- used for large spans
- used in steel bridges as main girder
- used in factories as rafter
2-Checking table:
It is a model made to study the effect of dynamic loads and earthquakes
on structures.
3a-Local axis:
It is the axis dealing with each member of the structure individually
b-Global axis:
It is the axis dealing with the whole structure .
1
-To transform from local to global or the inverse transformation matrix must be
used where :
g
l
{ D }DOFx1 = [ T ]DOF xDOF { d }DOFx1
t*
Ø
Ø
Ø
Ø
t*
Ø
Ø
Ø
Ø
t*
Ø
Ø
Ø
Ø
t*
And
where
t* =
T =
lx
mx
nx
ly
my
ny
Lz
mz
nz
Ø =
0
0
0
0
0
0
0
0
0
- where ( lx, mx, nx) , ( ly, my, ny ) , ( lz, mz, nz) are the cosines of angles between
local and global axis X, Y, Z .
4-Stiffness matrix method :
It is a displacement method which solve indeterminate skeletal and nonskeletal structures due to loads and environmental changes such as temperature
and settlement .
-steps of solution of grids :
1-Modeling
2- Overall load vector
3-Overall stiffness matrix
4-equilibrium equation
5-solving equilibrium equation
6-finding internal forces
2
B- Find the load vector for the given space truss.
1- Modeling:
NN = 18
NM = 37
DOF = 3x14 = 42
{F} =[K]
42x1
42x42
{D}
42x1
2- Overall load vector :
{F}
= 0 5 -8
0 5 -10
0 5 -10
42x1
{
000
6 5 -10
0 6 -8
000
0 -5 -10
0 -5 -10
3
000
0 0 0 b 0 5 -10
0 -5 -10
-6 -5 -10
}T
Q2- find the internal force in all members for the given grid
structure :
1-Modeling:
NN = 4
NM = 3
DOF = 3x1 = 3
{F} =[K] {D}
3x1
3x3
3x1
2- Overall load vector :
{F}
{ -13
3x1 = -
4.50 -0.67
}
T
2- Overall stiffness matrix :
Mem.
1
2
3
Lcm Ө
C
600 0.0 1
600 0.0 1
600 90 0
S GJ/L 12EI/L³ 6EI/L³
0 50000
4.67
1400
0 50000
4.67
1400
1 50000
4.67
1400
4
4EI/L
560000
560000
560000
2EI/L
280000
280000
280000
Member 3:
g
-1400
0
-1400 560000
0
0
0
50000
4.67
Member 1:
0
1400
0
50000
0
1400
0
560000
4.67
[ K1 ]=
Member 2:
4.67
0
-1400
[ K2 ]=
[ K ]3x3 =
0
50000
0
-1400
0
560000
14
-1400
0
-1400
660000
0
0
0
1170000
{F} =[K] {D}
3x1
3x3
3x1
5
[ K3 ]=
Q3 :Find the load vector for
the given space frame
1- Modeling :
NN = 10
NM = 10
DOF = 6 x 4 = 24
{F} =[K]
24x1
24x24
{D}
24x24
2- Overall load vector :
{F}
24x1
=
{6
3 -7 -4.5 5.33 7.5
0 0
-9 -4.5
-6
-2 3 - 7 -4.5 -5.33 -1.5
0
8 4 -9 -4.5
6
6
0
}
T