Upload
doanhuong
View
251
Download
7
Embed Size (px)
Citation preview
Chapter 22
Idealized Structure
• In real sense exact analysis of a structure
can never be carried out.
• Estimates have always to be made of the
loadings and strength of materials.
• Furthermore, points of application for
the loadings must be estimated.
• Models or idealization should be made.
Principle of superposition
• The total displacement or internal loadings
(stress) at a point in a structure subjected to
several external loadings can be determined by
adding together the displacements or internal
loadings caused by each of the external loads
acting separately.
• Linear relationships among loads, stresses and
displacements
Chapter 224
Superposition requirements
• Material must be behave in a linear elastic
manner.
• The geometry of the structure must not
undergo significant change. Small
displacement theory applies.
Chapter 225
Chapter 227
Determinacy & Stability
• Determinacy: when all the forces in structure can
be determined from equilibrium equation , the
structure is referred to as statically determinate.
Structure having more unknown forces than
available equilibrium equations called statically
indeterminate
• If n is number of structure parts & r is number of
unknown forces:
r = 3n, statically determinate
r > 3n, statically indeterminate
degree 1
ateindetermin Statically )3(310
3
10
st
n
r
degree 1 ate,indetermin Statically )2(37
2
7
st
n
r
Chapter 230
Chapter 235
• Improper Constraints
This can occur if all the support reactions are concurrent at a
point.
0dP
Chapter 236
• This can occur also when the reactive forces are all parallel
In General
r < 3n, Then the structure is Unstable
r >= 3n, Also, Unstable if member reactions are
concurrent or parallel or some of the components
form a collapsible mechanism
Sable )2(38
2
8
cases no special
n
r
Unsable Bar concurrent are reactions three the)1(33
1
3
n
r
Chapter 238
Chapter 242
Application of Equation of Equilibrium
1. If not given, establish a suitable x - y coordinate system.
2. Draw a free body diagram (FBD) of the object under
analysis.
3. Apply the three equations of equilibrium to solve for the
unknowns.
Procedure steps
kA
A
kB
BM
kA
AF
y
y
y
yA
x
xx
4.13
05.3860sin60 0F
5.38
050)14()1(60cos60)10(60sin60 0
30
060cos60 0
y
Chapter 244
IbA
A
IbA
AF
IbN
NNM
y
y
x
xx
B
BBA
2700
05.13313500 0F
1070
05.1331 0
5.1331
0)10()4()5.3(3500 0
53
y
54
53
54
Chapter 248
IbA
A
AF
ftIbM
MM
IbC
CM
y
y
xx
A
AAat
y
yRightB
7600
08000400 0F
0 0
.72000
0)10(80006000)35(400 0
400
06000150
y
point
Chapter 250
kNA
A
kNA
AF
kNC
CM
kNC
CM
y
y
x
xx
x
xA
y
yRightB
4.9
0)(863 0F
87.9
0)(87.14 0
7.14
0)2(8)3(6)4(3)5.1( 0
3
0)1(620
54
y
53
Chapter 252
mkNM
MM
kNE
EF
EF
kNC
CM
kNA
AM
E
ErightD
y
y
xx
y
yLeftD
y
yLeftB
.33.5
0)4(33.5)2(8 0
33.5
067.6488 0
0 0
67.6
0)8(8)11(43 0
4
0)3(860
)(
y
)(
Chapter 254
kNA
A
kNA
AF
kNC
CM
kNC
CM
y
y
x
xx
x
xRightB
y
yA
120
045sin9.8445sin6.254240 0F
285
045cos9.8445cos6.25460180195 0
195
0)(9.84)5.4(60)3(240)6(0
240
0)5.4(45cos9.84)5.4(45cos9.84)5.1(45sin6.254
)5.4(45cos6.254)5.1(60)5.1(180)6( 0
y
2
23
Chapter 258