Chapter 2 1 Chapter 2 Analysis of Statically Determinate Structures
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Chapter 21
Chapter 2
Analysis of Statically
Determinate Structures
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.
Chapter 23
Support connection
• Pin support and pin connection
Chapter 24
• Fixed support & fixed connection
Chapter 25
• Roller support
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 210
Chapter 211
Support for coplanar structures
Chapter 212
Idealized Structure
Chapter 213
Chapter 214
Chapter 215
Chapter 216
Chapter 217
Chapter 218
Chapter 219
Chapter 220
Chapter 221
Chapter 222
Chapter 223
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 226
Equation of Equilibrium
• In x-y plane
0
0
0
o
y
x
M
F
F
Internal loading
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
Chapter 228
Classify determinate & indeterminate structure
eDeterminat Statically )1(33
1
3
n
r
degree 2
ateindetermin Statically )1(35
1
5
nd
n
r
edeterminat Statically )2(36
2
6
n
r
Chapter 229
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
degree 4
ateindetermin Statically )2(310
2
10
th
n
r
Chapter 231
Chapter 232
Chapter 233
Chapter 234
• Stability
Partial Constraints
case loading with thisunstablesatisfied benot will0 xF
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
Chapter 237
Classify The structure Stable or
Unstable
Sable )1(33
1
3
cases no special
n
r
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
Unsable )3(37
3
7
n
r
Chapter 239
Chapter 241
Application of
Equilibrium Equation
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
Chapter 243
Example 1
Determine the Reactions
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
Chapter 245
Example 2
Determine the Reactions
600
0)6(60)4(60 0
120
06060 0F
0 0
y
kNM
MM
kNA
A
AF
A
AA
x
x
xx
Chapter 246
Chapter 247
Example 3
Determine the Reactions
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
Chapter 249
Example 4
Determine the Reactions
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
Chapter 251
Example 4
Determine the Reactions
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
Chapter 253
Example 5
Determine the Reactions
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
Copyright © 2009 Pearson Prentice Hall Inc.
Chapter 257
Example 6
Determine the Reactions
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
Chapter 259
Problem 1Determine the Reactions
Chapter 260
Problem 2Determine the Reactions
Chapter 261
Problem 3Determine the Reactions
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