Skip to main content
C
Callum19951-Visitor
1-Visitor
March 11, 2022
Solved

Beam Bending Shear Force In Mathcad

  • March 11, 2022
  • 3 replies
  • 7757 views

Good Evening All,

 

I am currently in the process of putting together a simply supported beam bending sheet and I was wondering if anyone had any tips of how I can proceed. As you can see from the attached sheet so far I have got the following:

 

1.) enter section ID to obtain the properties.

2.) enter point loads and location in the vectors

3.)enter UDLs and start / end points in the vectors.

4.)Calculate the reaction forces.

 

I am now stuck when it comes to the shear force as a function of x. ideally I would want V(x) so i can integrate for the bending moment. From the examples I have seen online alot of the times the shear force is input as a piecewise function (IF x<a... and so on). 

 

Is there anyway so I can get a general expression for shear force that will work no matter what the point loads are / shear forces are and so I don't have to type it out fully each time. Also as this sheet may be used by others I don't want them to have to type in the equations incase of mistakes. 

 

My current thought process would be to possible calculate the shear force as two function V1(x)=point loads and V2(x)=UDLs. I could then define V(x) as the summation of the two to obtain an expression for V(x). But I am open to suggestions and thankyou in advance for any help. 

 

Best Regards, 

Callum 

Best answer by terryhendicott

Hi Callum,

 

Here is a  second worksheet that deals with uniform UDL's and Point Loads.

It is Australian Steel Code and beam sizes which should be adjusted for other countries.

Worksheet selects the suitable beam from a table by calculating the capacity of all beams, then picks the size good enough.

 

In practice Gravity, Live, and Crane loads are increased by factors of Safety that are different for each type of loading.

Also in practice the resistance is diminished by a material factor depending on material.

The sheet has some sample values.

 

How to handle multiple point loads to get shear equations is demonstrated.

 

Cheers

Terry

3 replies

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
March 11, 2022

Hi Callum,

 

Here is a start. A generic loaded beam worksheet.

Enter four vectors. Calculations adjust as size of entry vectors vary.

 

A point load can be applied as a short length of uniform loading.

 

Cheers

Terry

    T
    21-Topaz II
    terryhendicott21-Topaz IIAnswer
    21-Topaz II
    March 12, 2022

    Hi Callum,

     

    Here is a  second worksheet that deals with uniform UDL's and Point Loads.

    It is Australian Steel Code and beam sizes which should be adjusted for other countries.

    Worksheet selects the suitable beam from a table by calculating the capacity of all beams, then picks the size good enough.

     

    In practice Gravity, Live, and Crane loads are increased by factors of Safety that are different for each type of loading.

    Also in practice the resistance is diminished by a material factor depending on material.

    The sheet has some sample values.

     

    How to handle multiple point loads to get shear equations is demonstrated.

     

    Cheers

    Terry

      C
      Callum19951-VisitorAuthor
      1-Visitor
      March 12, 2022

      Hi Terry,

       

      Thanks for the example sheet, do you have any additional information about what the sheet is doing at each stage. I am relatively new to the software and any additional information would surely be appreciated. 

      CC_10223533_0-1647102862526.png

      Currently I have gone for this approach and obtained the correct shear force diagram but I would be interested to hear more about the sheet that you have provided. 

      CC_10223533_1-1647102945140.png

      CC_10223533_2-1647102969713.png

       

      Best regards,

      Callum

       

      C
      Callum19951-VisitorAuthor
      1-Visitor
      March 12, 2022

      for example I can't see how the start and end points of the UDLs are calculated or do you convert the UDLs to a point load and only use the UDL's that act over the entire beam. 

      K
      KevinFinity12-Amethyst
      12-Amethyst
      March 15, 2022

      By regular old statics, this can be derived:

      KevinFinity_1-1647372468508.png

      Your reaction at the first end of the beam is R1. This is also the first value of the shear equation.

      Then

      KevinFinity_3-1647372688191.png

       

      I hope this helps!

       

      ***

       

      Note: When your loading is a piecewise function, you don't have to use piecewise functions for your shear and bending moment equation, but that changes once you need to use boundary conditions for the angle and deflection equations. You will have to integrate by parts and it gets rather complicated. 

      Terms & ConditionsAccessibility statement