Master Shear Force Diagrams with this Helpful Homework Example

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Discussion Overview

The discussion revolves around the process of drawing Shear Force Diagrams (SFD) for a beam subjected to a uniformly distributed load (UDL). Participants are exploring the correct approach to start the diagram and how to account for the UDL in their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to begin the SFD due to the presence of a UDL, questioning whether to start at a specific value.
  • Another participant suggests that the left half of the diagram is correct but questions the expected change in shear force over a specific segment, indicating a potential error in the calculations.
  • A later reply confirms that the SFD should return to zero at the free end of the beam, reinforcing the concept that shear force and bending moment are zero at that point.
  • Participants discuss the challenges of drawing the diagram to scale, with one indicating limitations due to lack of resources at home.

Areas of Agreement / Disagreement

There is no clear consensus on the correct starting point for the SFD or the calculations involved, as participants express differing views on the accuracy of the initial attempts and the expected outcomes.

Contextual Notes

Participants mention potential errors in calculations and the importance of drawing to scale, but do not resolve the specific assumptions or steps needed to clarify the process fully.

Who May Find This Useful

This discussion may be useful for students learning about shear force diagrams, particularly those encountering uniformly distributed loads in their homework or projects.

ryanmcarthy
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Homework Statement


Hi,
I know how to draw simple Shear Force Diagrams, but I am struggling with the example in the below picture, as it has a UDL.


Homework Equations



ShearForce2.jpg



The Attempt at a Solution



Normally for the solution, I should start the diagram at 26.7, then across and down to 16.7, then across and up to 70, then across and down to 50.

But as it has a UDL I know this changes things! How do I start the diagram, and I will have a go at doing it. Do I start at 26.7, or do I need to do something before this?


Thanks a lot
 
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I've come up with this, but don't know if I started correctly?

Diagram1.jpg
 
The left half is correct. In the 5m stretch between the 10 kN load and the Reaction R2, what would you expect the change of shear force to be? The figure of -28.7 seems wrong to me. As the final result on the right is not 20 kN, you know you have gone wrong. I recommend you draw this to scale on squared paper. In that case, you should see the gradient of the graph is the same throughout.
 
Thanks a lot for the relpy! I can't draw it on square paper, as I am at home and don't have a scanner (only at work).

Is this attempt better? I'm not sure if I need to go down to zero at the end though?

ShearForce3.jpg


Thanks
 
That is now correct, you can check your answer here,

http://learntoengineer.com/beam?f=2,u1|8,u2|3,-10|10,-20&d=0,10!-5&m=

The SFD does have to go back down to 0 at the end. The shear force and bending moment of any beam is 0 at a free end.
 
Last edited by a moderator:
Hi,

Thanks a lot for the help!
 

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