Analysis of statically Indeterminate structures by the Force

Analysis of statically Indeterminate structures by the Force

Analysis of statically Indeterminate structures by the Force Method Part 2 Example 1 aw B.M.D & S.F.D for the following indeterminate stru 5wL4 5 1404 33333.3 B

384EI 384EI EI f BB RB L3 1(40)3 1333.3 48EI 48EI

EI B RB f BB 0 33333.3 1333.3 RB 0 EI EI RB 25 k S.F.D

B.M.D Note 3 B B y f BB C y f BC 0 C B y f CB C y f CC 0 Example 2 Find the reactions at B & C for the following indeterminate structure 12 4 4 97 365

C 4 EI EI 2 3 EI

24 8 8 97 520 B 8 EI EI 2 3 EI Conjugate beam

40.8 1.7 4 4 11 .33 f CB ( ) 4 EI EI EI 2 3 13.6 8 11 .33 54.4 f BB 8

EI 3 EI EI f CC Conjugate beam f BC Conjugate beam 5.8 4 11 .6 38.67

4 EI 3 EI EI 43.5 1.45 6 6 8.7 ( ) 6 EI EI 2 3 EI B B y f BB C y f BC 0

520 54.4 43.5 By Cy 0 EI EI EI C B y f CB C y f CC 0 365 40.8 38.67

By Cy 0 EI EI EI By Cy Example 3 Find the reactions at A & B for the following indeterminate structure

A M A AA M B AB 0 B M A BA M B BB 0 3 3wL3 3 2 20 375 A 128EI 128EI EI

3 7 wL3 7 2 20 291.7 B 384 EI 384 EI EI ML 1 20 6.67

3EI 3EI EI ML 1 20 6.67 3EI 3EI EI ML 1 20 3.33 BA

6 EI 3EI EI BB AA AB A M A AA M B AB 0 375 6.67 3.33 MA MB

EI EI EI B M A BA M B BB 0 291.7 3.33 6.67 MA MB EI EI EI M A 45.8 k

M A 20.8 k Example 4 aw B.M.D & S.F.D for the following indeterminate stru B M B BB 0 B B ' B " BB 'BB "BB wL3 B 24 EI

PL2 B 16 EI ML BB 3EI ML BB 3EI 3

12012 8640 24 EI EI 2 50010 3125 16 EI

EI 112 4 3EI EI 110 3.33 3EI EI 8640 3125 11765 B

EI EI EI 4 3.33 7.33 BB EI EI EI B M B BB 0 11765

7.33 MB 0 EI EI M B 1602 Force Method Analysis: Frames Find the reactions at A & B for the following indeterminate structure Based on virtual work method (deflection calculation)

83.33 166.7 B 2 EI EI f BB 10 8 48 2.66

2.66 EI EI EI B Bx f BB 0 166.7 48 Bx 0 EI EI Bx 3.47 kN

Ax 3.47 kN B y 22.8 kN Ay 17.2 kN Example 5 Find Cy for the following indeterminate structure Based on virtual work method (deflection calculation) 640 1920 C

3 EI EI f CC 18 24 168 4 4 EI EI

EI C C y f CC 0 1920 168 Cy 0 EI EI C y 11 .43 kN Group work 1 Find Cy for the following indeterminate

structure

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