three moment theorem

ThreeMomentTheoremHomework 06Lab 04

ThreeMomentTheoremHomework 06

Use the Three Moment Theorem to determine all reactions and support moments for the given continuous beam.

Datasheet Span ASpan BSpan CUniform load on span A, w1Uniform load on span C, w2Point load on span b, PDistance to point load P from R2, D

28FT21FT24FT4KLF5KLF

60K14FT

Questions 1. Moment at support R1, M1 (- if tension on top)2. EI Theta on left side of R23. EI Theta on right side of R24. Moment at support R4, M4 (- if tension on top)5. EI Theta on left side of R36. EI Theta on right side of R37. Moment at support R2, M2 (- if tension on top)8. Moment at support R3, M3 (- if tension on top)9. Support reaction, R1 (- if downward)10. Support reaction, R2 (- if downward)11. Support reaction, R3 (- if downward)12. Support reaction, R4 (- if downward)

ThreeMomentTheoremHomework 06




60K14FT


Main Steps1. Calculating M2, M3

Three Moment Theorem

2. Calculating R1, R2, R3, R4Equilibrium Theory, ΣM, ΣV

1. Calculating M2, M3 Three Moment Theorem

Related Questions 1. Moment at support R1, M1 (- if tension on top)2. EI Theta on left side of R23. EI Theta on right side of R24. Moment at support R4, M4 (- if tension on top)5. EI Theta on left side of R36. EI Theta on right side of R37. Moment at support R2, M2 (- if tension on top)8. Moment at support R3, M3 (- if tension on top)



60K14FT

0 + 2 x M2 x (28 + 21) + M3 x 21 = 6 x (3658.67 + 1306.67)M3 = (29792-98 M2)/21

MA = 0MB = M2MC = M3

L1 = 28L2 = 21

EIθ1 = wL13/24 = 4 x 283 / 24 = 3658.67

EIθ2 = 4PL22/81 = 4 x 60 x 213 / 81 = 1306.67

( ) [ ]212211 62 Θ+Θ=+++ EIEILMLLMLM CBA

1. Calculating M2, M3 Three Moment Theorem

Related Questions 1. Moment at support R1, M1 (- if tension on top)2. EI Theta on left side of R23. EI Theta on right side of R24. Moment at support R4, M4 (- if tension on top)5. EI Theta on left side of R36. EI Theta on right side of R37. Moment at support R2, M2 (- if tension on top)8. Moment at support R3, M3 (- if tension on top)



60K14FT

M2 x 21 + M3 x (21 + 24) = 6 x (1653.75 + 2880)Plugin M3 = (29792-98 M2)/21M2 = 251.82 K-FT (-, Tension on Top)M3 = 243.51 K-FT (-, Tension on Top)

MA = M2MB = M3MC = 0

L1 = 21L2 = 24

EIθ1 = 5PL22/81 = 5 x 60 x 213 / 81 = 1653.75

EIθ2 = wL13/24 = 5 x 243 / 24 = 2880

( ) [ ]212211 62 Θ+Θ=+++ EIEILMLLMLM CBA


Related Questions 9. Support reaction, R1 (- if downward)10. Support reaction, R2 (- if downward)11. Support reaction, R3 (- if downward)12. Support reaction, R4 (- if downward)

Datasheet Span ASpan BSpan CUniform load on span A, w1Uniform load on span C, w2Point load on span b, PDistance to point load P from R2, D|M2| = 251.82 K-FT|M3| = 243.51 K-FT


60K14FT





60K14FT

FBD1:∑M@R2 = 0 = R1 x L1 – (w1 x L1

2)/2 + M2= R1 x 28 - (4 x 282)/2 + 251.82

R1 = 47.01 K∑V = 0 = R1 – w1 x L1 + V2

= 47.01 – 4 x 28 + V2V2 = 64.99 K





60K14FT

FBD2:∑M@R3 = 0 = - M2 - V2 x L2 + R2 x L2 – P x (L2 – D) + M3

= - 251.82 – 64.99 x 21 + R2 x 21 – 60 x (21 – 14) + 243.51 R2 = 85.39 K

∑V = 0 = - V2 + R2 - P + V3= -64.99 + 85.39 – 60 + V3

V3 = 39.6 K





60K14FT

FBD3:∑M@R4 = 0 = - M3 – V3 x L3 + R3 x L3 – (w2 x L3

2)/2 = - 243.51 – 39.6 x 24 + R3 x 24 – (5 x 242)/2

R3 = 109.75 K∑V = 0 = - V3 + R3 - w2 x L3 + R4

= -39.6 + 109.75 – 5 x 24 + R4R4 = 49.85 K

Main Steps1. Calculating M2, M3

Three Moment Theorem





60K14FT


https://miro.com/app/board/o9J_lR5H5iY=/

Lab 04

ThreeMomentTheorem

Watch the Video First !

three moment theorem

Documents