Shear Force Bending Moment

This function SFBM.m calculates and draw the shear force and bending moment diagrams.

%% 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 the 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()

[maxshearforce, loc_maxsf] = prob.GetMaxShearForce()

[maxbendmoment, loc_maxbm] = prob.GetMaxBendMoment()

%% 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()

[maxshearforce, loc_maxsf] = prob.GetMaxShearForce()

[maxbendmoment, loc_maxbm] = prob.GetMaxBendMoment()

%% Example(4)

%Problem Name

Name = 'Example 4';

% Length and Supports

Length = 20; Supports = [5,20]; % length = 20m, supports at 5m and 20m;

prob = SFBMProb(Name, Length, Supports);

% Concentrated Loads

prob.AddPointLoad(-2, 0); % 2N downward at point 0

% Torques

prob.AddMoment(50, 8); % ACW 50Nm at point 8

prob.AddMoment(-45, 15); % CW 45Nm at point 15

% Distributed Loads

prob.AddDistLoad([5, 5], [1,3]); % Constant 7N/m upwards from 1m to 3m

prob.AddDistLoad([-4, -4], [14, 17]); % Constant 5N/m downwards from 12m to 18m

% Solve the problem

prob.Solve()

[maxshearforce, loc_maxsf] = prob.GetMaxShearForce()

[maxbendmoment, loc_maxbm] = prob.GetMaxBendMoment()

%% 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()

[maxshearforce, loc_maxsf] = prob.GetMaxShearForce()

[maxbendmoment, loc_maxbm] = prob.GetMaxBendMoment()