Mechanics of Solids

Mechanical Engineering Department, Indian Institute of Technology Kharagpur

This is a repository of some useful files for the subject "Mechanics of Solids" in the Mechanical Engineering Department of IIT Kharagpur. This subject is a mandatory one for the second year undergraduate students of Mechanical Engineering.

The latest version of the course home page is maintained at: http://www.facweb.iitkgp.ac.in/~jeevanjyoti/teaching/mechsolids/2021/

• Tutorial Sheet 2A: Q3

• Tutorial Sheet 2A: Q7

• Tutorial Sheet 2A: Q8

• Tutorial Sheet 2A: Q9

• Mohr Circle

• Tutorial Sheet 5: Q13: Polar Strain-Displacement

• Stress equilibrium equations in cylindrical coordinates

Manual to use the Beam class

Simply install the package using the following command and use the Beam class as shown below:

pip install Lib-mechsolids-abhinav==0.0.1

OR if you are forking the repository and want to do things manually, then make sure to have the following libraries

We need to have Sympy installed before using the beam class. To install Sympy, use the following command:

pip install sympy

• Tested with Sympy version 1.11.1
• Tested with Python version 3.9.13
• Tested with Matplotlib version 3.5.2
• Tested with Numpy version 1.21.5

Steps to use the Beam class:

1. Create a new Python file to solve a problem. Import the Beam and math modules as follows:

   from Beam import *
   from math_functions import *
   

2. Create either a Simply Supported Beam or a Cantilever Beam object as follows:

   beam = SimplySupportedBeam(NameOfBeam, LengthOfBeam)
   beam = CantileverBeam(NameOfBeam, LengthOfBeam)
   

3. If the beam is a Simply Supported Beam, then add the supports as follows:

   beam.add_supports(Support(PositionOfSupport1, PositionOfSupport2))
   

   where position is the distance of the support from the left end of the beam.

4. Create loads using the load class as follows:

   load1 = PointLoad(ValueOfLoad, PositionOfLoad)
   load2 = DistributedLoad(StartPosition, EndPosition, LoadAtStart, LoadAtEnd)
   load3 = EquationLoad(EquationString, StartPosition, EndPosition, startLoad(=0), endLoad(optional))
   
   # add these loads on the beam
   beam.add_load(load1)
   beam.add_load(load2)
   beam.add_load(load3)
   

   where position is the distance of the load from the left end of the beam.

5. To generate the shear force and bending moment diagrams, use the following functions:

   beam.plot_sfd_and_bmd()
   # if you want to plot just the shear force diagram or bending moment diagram, use the following functions:
   beam.plot_sfd()
   beam.plot_bmd()