Prepaid by: 130670106502 130670106503

Review Conjugate beam

method

Review Conjugate beam

method

Con

jug

ate

-Beam

Su

pp

ort

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(35

1

5

nd

n

r

degree 4

ateindetermin Statically )2(310

2

10

th

n

r

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