Shear Force & Bending Moment Examples

 This program calculates the shear force and bending moment profiles, 
 draws the free body, shear force and bending moment diagrams of the 
 problem.

 Under the free body diagram, the equations of each section is clearly 
 written with Latex

How to call the function

 To use this program, you need to call the solve function on the instance 
 of the SFBMProb object that has the complete problem description.
 You first create the SFBMProb Object and then add the loads in no
 partcular order. 

How to create the SFBMProb object

 create an instance of SFBMProb by calling "SFBMProb" with three
 arguments. The first is the name of the problem. For instance, 
 "Example 1", the second argument is Length of the beam, and the third
 is locations of the supports. 

 prob = SFBMProb(name, length, supports)

Cantilever

   If the problem is a cantilever problem, then you have only one clamped 
   support, at the beginning or end of the beam. In such a case, the number is
   second argument contains 2 elements instead of three. 

   For instance, for a cantilever of length 20m, supported at the beginning, 
   prob = SFBMProb("Cantilever", 20, 0)

and if supported at the end, prob = SFBMProb("Cantilever", 20, 20)

Beam on the floor

   Its possible to have a problem in which the body is lying on the floor 
   without any point support. In such scenario, 
   prob = SFBMProb("BeamOnFloor", 20, [])

Set Units

 We have just two primary physical quantities here: Force and Legnth.
 ForceUnit default is KN
 LengthUnit default is m

 but to set a preferred unit, use

 prob.ForceUnit = "lb";
 prob.LengthUnit = "inch";

Load Description

 Loads can be Force: such point or distributed load, or Torque that we
 call Moment here. In general Load would have value and location.
 The sign of the value can indicate whether it is pointing upwards, or
 downwards in the case of force, or clockwise/anticlockwise in case of
 moment. While moment and point load have scalars for value and
 location, distributed load have vector of value and location. 

How to add loads to the object.

Moment(Torque)

     To add a clockwise moment of magnitude 3KN-m applied at point 5m
     prob.AddMomentLoad(-3, 5);
     For an anticlockwise moment of magnitude 7KN-m applied at point 8m
     prob.AddMomentLoad(7, 8);

Concentrated Load(Force)

     To add a downward point load of magnitude 0.8KN applied at point 3m
     prob.AddPointLoad(-0.8, 3);
     For an upward point load of magnitude 5KN-m applied at point 7m
     prob.AddMomentLoad(5, 7);

Distributed Force

     To add uniform upward distributed load of magnitude 2KN/m applied from point 3 to 5m 
     prob.AddDistLoad([2, 2], [3, 5])
     For linearly increasing distributed load 2KN/m  to 5KN/m applied from point 3 to 5m 
     prob.AddDistLoad([2, 5], [3, 5]);

Example(1)

    -Problem Name
    Name = 'Example 1';
    
    -Length and Supports
    Length = 10; Supports = [2, 10]; % length  = 10, supports at 2 and 10;
    prob = SFBMProb(Name, Length, Supports);

    -Set Unit
    prob.ForceUnit = "lb";
    prob.LengthUnit = "inch";
    
    -Concetrated Loads
    prob.AddPointLoad(-5, 0); % 5N downward at point 0
    prob.AddPointLoad(-10, 8); % 10N downward at point 8

    -Torques
    prob.AddMoment(10, 3);  % ACW 10Nm at point 3
    prob.AddMoment(-10, 7); % CW 10Nm at point 7

    -Solve the problem
    prob.Solve()

Example(2)

    -Problem Name
    Name = 'Example 2';
    
    -Length and Supports
    Length = 20; Supports = 0; % length  = 20m, Cantilever supported at 0 m;
    prob = SFBMProb(Name, Length, Supports);
    
    -Concentrated Loads
    prob.AddPointLoad(-5, 6);   % 5N downward at point 6
    prob.AddPointLoad(-10, 13); % 10N downward at point 13
    
    -Distributed Loads
    prob.AddDistLoad([5,5],[1,3]);    % Constant 5N/m upwards from 1m to 3 m 
    prob.AddDistLoad([-4,-4],[14,17]); % Constant 4N/m downwards from 14m to 17 m
    
    -Solve the problem
    prob.Solve()

Example(3)

    -Problem Name
    Name = 'Example 3';
    Length and Supports
    Length = 30; Supports = [0,20]; % length  = 30m, supports at 0m and 20m;
    prob = SFBMProb(Name, Length, Supports);
    
    -Concentrated Loads
    prob.AddPointLoad(-20, 6);   % 20N downward at point 6
    prob.AddPointLoad(-10, 13);  % 10N downward at point 13
    prob.AddPointLoad(5, 27);    % 5N upward at point 27
    
    -Torques
    prob.AddMoment(50, 8);  % ACW 50Nm at point 8
    prob.AddMoment(-45, 25); % CW 45Nm at point 25
    
    -Distributed Loads
    prob.AddDistLoad([7, 7], [1,3]);    % Constant 7N/m upwards from 1m to 3m 
    prob.AddDistLoad([-5,-5], [12,18]); % Constant 5N/m downwards from 12m to 18m
    
    -Solve the problem
    prob.Solve()

Example(4)

    -Problem Name
    Name = 'Example 4';
    
    -Length and Supports
    Length = 20; Supports = [6,20]; % length  = 20m, supports at 5m and 20m;
    prob = SFBMProb(Name, Length, Supports);
    
    -Concetrated Loads
    prob.AddPointLoad(-2,0);  % 2N downward at point 0
    
    -Torques
    prob.AddMoment(10,8);   % ACW 10Nm at point 8
    prob.AddMoment(-15,12); % CW 10Nm at point 12
    
    -Distributed Loads
    prob.AddDistLoad([5, 2, 5], [1, 3, 5]);    % Constant 5N/m upwards from 1m to 3m and 
    prob.AddDistLoad([-4, -2, -4],[14, 16, 18]); % Constant 4N/m downwards from 14m to 17m
    
    -Solve the problem
    prob.Solve()