Finding shear force and bending moment in a beam

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SUMMARY

The discussion focuses on calculating shear force (Vx) and bending moment (Mx) in a beam segment between points C and D. The support reactions were identified as RA = 5kN and RB = 55kN. The equations of equilibrium used include ƩFy = 0 and ƩMx = 0. Participants emphasized the importance of utilizing free body diagrams to simplify the calculations and suggested using point D as the origin for measuring distances to accurately determine the shear force and bending moment.

PREREQUISITES
  • Understanding of static equilibrium principles in mechanics
  • Familiarity with shear force and bending moment diagrams
  • Knowledge of free body diagram construction
  • Basic algebra for solving equations
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  • Study the construction of free body diagrams for beam analysis
  • Learn how to derive shear force and bending moment equations from equilibrium conditions
  • Explore examples of beam loading scenarios and their corresponding shear and moment diagrams
  • Investigate the effects of different support types on shear and moment calculations
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Engineering students, structural analysts, and professionals involved in mechanical design or civil engineering who need to calculate shear forces and bending moments in beams.

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Homework Statement



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I am attempting to calculate the shear force Vx, and bending moment Mx within the interval C - D of this beam.

Homework Equations



ƩFy = 0
ƩMx = 0

The Attempt at a Solution



I have calculated the support reactions to be RA = 5kN and RB = 55kN

ƩFy = 0

5 + 55 - 10(x-4) - 10 - Vx = 0

ƩMx = 0

5x + 55(x-4) - 10(x-2) - 10((x-4)^2/2) - Mx = 0

I'm really not sure if this is correct or not! Any help would be greatly appreciated :)

Thanks all
 
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These are not correct, it is easier to draw free body diagrams which cut through CD about the RIGHT end of the beam. The shear will jump right out at you. And for the moment in between C-D, use D as the origin of your x value, right to left for x.
 

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