Structure Analysis II

Analysis of statically

Indeterminate structures by the

Force MethodPart 1

Review Conjugate beam

method

Con

juga

te-B

eam

Sup

port

s

EIEIM

EIV

BB

BB

5.14062)25(5.562

5.562

'

'

Review Example 1Find the deflection at Point B

Review Example 2

EIEIEIMCC

162)3(63)1(27'

Find the deflection at Point C

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 2

ateindetermin Statically )1(3515

nd

nr

degree 4

ateindetermin Statically )2(310210

th

nr

Force Method: General Procedure

1.Determine the number of redundant reactions

2.Remove enough redundants to form a determinate structure

3.Calculate the displacements that the known loads cause in the determinate structure

4.Calculate displacements at the same points in the determinate structure due to the redundants

5.The sum of the displacements calculated in steps (3) and (4) must be equal to the displacements at the actual indeterminate structure

6.Use equilibrium to determine the remaining reactions

0

0

BByB

BByBB

BBB

fB

fB

tcoefficienyflexibilitfBB

+

Note 1

Compatibility Equation

+

0

0

AAAA

AAAAA

AAA

M

M

tcoefficienyflexibilitAA

Note 2

Compatibility Equation

Note 3

0

0

CCyCByC

BCyBByB

fCfB

fCfB

Force Method of Analysis: Beams

Example 1Determine the reaction at the roller support B of the beam shown

Solution

Compatibility Equation

0 BByB fB

0 BByB fB

EIEIB900010900

Conjugate beam

method

EIEIEI

PLfBB576

3121

3

33

kN 6.15

05769000

0

y

y

BByB

BEI

BEI

fB

Determine the reaction at the roller support B of the beam shown, the support B settles 1.5 in

Example 2

125.1 BByB fBCompatibility Equation

EIEIEIBB

BByB

M

fB3168014401800

125.1

)8()24(

EIEIEIBBB mf 2304144144 )8()24(

56.5 750

)10(294

3

125.1230431680

125.1

y

EIyEI

BByB

BinI

ksiE

B

fB

Determine the moment at fixed wall for the beam shown

Example 3

Solution

EIA3.33

EIAA33.3

k.ft 1000

33.33.33

A

EIAEI

AAAA

MMM

Conjugate beam method