Mechanics Of MaterialsSlope and Deflection of Simply

Supported Beams

ANKIT SOOD

CHRISTINA MAYINI

DHEER VEER VIKRAM SINGH

HITESH SOOD

SIDDHARTH MAHAJAN

VISHAL MISHRA

The purpose of this calculation is to obtain information about shear, bending moment, and deflection distribution over the length of a beam, which is under various transverse loads: couples, concentrated and linearly distributed loads. The result of calculation is represented by shear force, bending moment and deflection diagrams.

The material of the beam is linear-elastic and isotropic with elasticity modulus E.

All loads are lateral (forces or moments have their vectors perpendicular to the beam axis) and acting at the same plane. All deflections occur in this plane of bending.

Deflections are small compared to the length of the beam. In this case we apply equilibrium equations to the unreformed beam axis (or its parts) and assume that the curvature of the deformed beam axis is equal to the second derivative of the deflection function.

ASSUMPTIONS

RELATION BETWEEN LOADING, S.F, B.M, SLOPE AND DEFLECTION

Consider a simply supported uniform section beam with a single load F at the centre.   

SM 104 beam apparatus MKIII

DEFLECTION

The beam will be deflect symmetrically about the centre line with zero slope (dy/dx) at the centre line.   It is convenient to select the origin at the centre line.

Consider a simply supported uniform section beam with a Concentrated Load and UDLThe B.M Equation is:

ab

c

l

W1wb c

w6

b c 3

b+

c

PROJECT CASE CONSIDERATION

Note that Macaulay terms are integrated with respect to, for example, (x -a) and they must be ignored when negative. Substitution of end conditions will then yield the values of the constants A and B in the normal way and hence the required values of slope or deflection.

SLOPE AND DEFLECTION GRAPHS

Simply supported beams when subjected to multiple loadings yields graphs of these nature