Shear Diagram - Beam with 3 supports

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Discussion Overview

The discussion revolves around drawing the shear diagram for a compound supported beam with three supports. Participants are exploring the application of static equilibrium equations to solve for reactions and moments at various points on the beam.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes their approach to summing forces and moments but encounters issues with variables canceling out, leading to an equation of 0 = 0.
  • Another participant suggests splitting the beam into two parts and writing separate equations of static equilibrium for each section.
  • There is a question about whether the bending moment at point C is zero, with some participants affirming that the pin cannot develop a moment.
  • One participant expresses confusion about the relationship between the upward force at pin C and the shear force at C.
  • A participant raises a query about the correctness of generating equations by taking moments about points A and B, seeking clarification.
  • Another participant notes that the original poster has not been active for a long time and advises against resurrecting old posts, suggesting that new threads should be started for specific questions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the bending moment at point C and the relationship between forces and shear at that point. There is no consensus on the best approach to solve the problem, as different methods are proposed and debated.

Contextual Notes

Some participants mention limitations in their equations and the potential for misunderstanding the relationships between forces and moments, particularly at the pinned joint.

teeth
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Homework Statement


Draw the shear diagram for the compound supported beam.
7uMqg.png


Homework Equations



Statics... so sum of moments at any point or forces in any direction are 0

The Attempt at a Solution



I summed the forces in the y direction, as well as the moments at A and moments at B, but using these 3 equations causes the variables to cancel out when solving for the reactions. I get 0 = 0...
I guess I cannot use two moment equations, but then how am I to solve this? I'm in first year statics.

My equations are...
0 = \sum F_y = A_y + B_y + D_y -3*6 - 5
0 = \sum M_A = B_y*3 + D_y*9 -3*6*3 - 5*7.5
0 = \sum M_B = -A_y*3 + D_y*6 - 5*4.5
Counter-clockwise moment is positive
 
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You have a pinned joint at point C. Try splitting the single beam into two parts: A-B-C and C-D. Write separate equations of static equilibrium for each piece of the beam. What's the bending moment at point C?
 
Sorry, is the bending moment at C zero?
I tried getting isolating for C_y but I keep getting C_y = 0
Is the upward force at pin C the same as the "shear force" at C?
 
teeth said:
Sorry, is the bending moment at C zero?

Yes. The pin cannot develop a moment.

I tried getting isolating for C_y but I keep getting C_y = 0
Is the upward force at pin C the same as the "shear force" at C?

If you write equilibrium equations for beam C-D, you'll see that Cy cannot be zero.
 
teeth said:

Homework Statement


Draw the shear diagram for the compound supported beam.
7uMqg.png


Homework Equations



Statics... so sum of moments at any point or forces in any direction are 0

The Attempt at a Solution



I summed the forces in the y direction, as well as the moments at A and moments at B, but using these 3 equations causes the variables to cancel out when solving for the reactions. I get 0 = 0...
I guess I cannot use two moment equations, but then how am I to solve this? I'm in first year statics.

My equations are...
0 = \sum F_y = A_y + B_y + D_y -3*6 - 5
0 = \sum M_A = B_y*3 + D_y*9 -3*6*3 - 5*7.5
0 = \sum M_B = -A_y*3 + D_y*6 - 5*4.5
Counter-clockwise moment is positive

Hi Teeth, I had a query.

By taking the moments about Point A and B, You have formulated the equations 2 and 3.
Is this way of generating equations right ?

Looking forward to a reply from you soon.

Aman Ratan
Thanks
 
Aman Ratan said:
Hi Teeth, I had a query.

By taking the moments about Point A and B, You have formulated the equations 2 and 3.
Is this way of generating equations right ?

Looking forward to a reply from you soon.

Aman Ratan
Thanks
Teeth hasn't been around PF since posting this question a year and a half ago, so I hope you are not looking for a reply any time soon.

PF generally frowns on resurrecting old posts like this.

It is OK to link to an old post if you have a particular question about it, but you should start your own thread in that case.
 
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SteamKing said:
Teeth hasn't been around PF since posting this question a year and a half ago, so I hope you are not looking for a reply any time soon.

PF generally frowns on resurrecting old posts like this.

It is OK to link to an old post if you have a particular question about it, but you should start your own thread in that case.

Thanks SteamKing
 

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