To determine the central deflection of a simply supported beam loaded by a concentrated load at mid point

To determine the central deflection of a simply supported beam loaded by a concentrated load at mid point

Apparatus:

Deflection of beam apparatus, Hanger and weights, Meter rod, Dial indicator, Vernier Calipers

Deflection of beam apparatus contains a metal beam and two knife-edge supports upon which the beam is supported for this experiment and hence the beam becomes of a simply – supported type. 

Summary of Theory: 

Beams are structural members supporting loads applied at various points along the members. A beam undergoes bending by the loads applied perpendicular to their axis of the structure. Beams are of various types.

If the supports are at the ends such that one of them is pin and other is roller then such a beam is called simply supported beam. The supports can be considered as simple wedges at the ends as shown in figure (a).

Consider a simply supported beam AB of length “L” and carrying a point load “W” at the centre of beam C as shown in figure (b).

The maximum deflection for simply supported beam will occur at half the distance from either support (mid-point). 

Let

 = Deflection of beam at any point along the length of the beam

 = Central deflection of a beam

X= variable distance from end B

From the symmetry of the figure, we find that the reaction at A is:

R_A = R_B  = W/2

The maximum deflection y_c at x= L/2 is given by:

Where E = Modulus of elasticity for the material of beam

I = Moment of inertia of the beam

Load Deflection Curve:

Procedure:   

1. Set the Deflection of Beam apparatus on a horizontal surface.

2. Set the dial indicator at zero.

3. Apply a load of 1N and measure the deflection using dial indicator.

4. Take a set of at least five readings of increasing value of load and then take readings                   on  unloading.

5. Calculate the “Modulus of Elasticity (E)” of the material of the beam.

Observations and Calculations:

Least Count of the dial indicator    = __________ mm

Effective length of beam (L)    =__________ m

Breadth of beam (b)     =__________ m

Height of beam (h)     =__________ m

Moment of inertia of the beam (I=bh³/12)  =__________ m

Table of Observations:

No of Obs.	Effective Load-W (N)	Central Deflection- (mm)			W/ (N/mm) From Graph	Modulus of Elasticity (MPa)
		Loading	Unloading	Average
1
2
3
4
5
6
7