EXPERIMENT # $2$: Analyze and draw the Shear force and Bending Moment Diagram for cantilever beam using SAP $2000.$

Objectives

To determine manually the reactions and draw shear force and bending moment diagram for cantilever beam.

To determine the reactions and draw shear force and bending moment diagram for cantilever beam using SAP $2000$ program.

To compare the result of manual analysis and SAP $2000.$

Theory:

A cantilever is a rigid structural element that extends horizontally and is unsupported at one end. Typically, it extends from a flat vertical surface such as a wall, to which it must be firmly attached.

Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab.

Shear force refers to the force that acts parallel to the cross$-$section of a structural element, while bending moment is the moment that occurs when an external force is applied to the element causing it to bend.

Equations of Static Equilibrium:

A structure is said to be in equilibrium, if it is initially at rest, so it will remain at rest when subjected to a system of forces and moments.

If a body is in equilibrium, then all its members and parts are also in equilibrium.

For the body or structure, to be in equilibrium, the following three equations must be satisfied.

EGCV $2220-$ Structural Analysis $1$

Page $2$

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$;$,{\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0$;$,{\displaystyle \underset{?}{\overset{?}{}}}{M}_z=0$

Problem: A Cantilever beam of span $2m$ is loaded with concentrated loads of intensity $20kN$ at free end and a uniformly distributed load of intensity $15k\frac{N}{m}$ over full span. Calculate the reactions at support and draw Shear force and Bending Moment diagram.

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Step $1$: Calculate the reactions using equilibrium equations.

Step $2$: Calculate the shear$-$force ordinates at support and load points.

Step $3$: Calculate the Bending moment values at support and load points.

Step $4$: Draw the Shear$-$force and bending moment diagrams.

Step $5$: Draw Shear$-$force and Bending moment diagrams Using SAP $2000.$

Step $6$: Compare the results of Manual calculation and SAP $2000$

Calculation:

EGCV $2220-$ Structural Analysis I

$\backslash$table$[[,$R$1($kN$),$R$2($kN$),$Maximum B$.$M$,\backslash$table$[[$Maximum$],[$S$.$F$]]],[$Manual$,,,,],[$SAP $2000,,,,]]$

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