Table 1: Modulus of Rigidity of some material
Materials Modulus of Rigidity (GPa)
Aluminium Alloys 27
Brass 40
Copper 45
Lead 13.1
Rubber 0.0003
Tungsten 161
RUBBERS:
Rubber is an elastic material that can be produced naturally from various plant sources or
synthetically through a variety of chemical processes. It has been in use for thousands of years,
during which time it has been produced in numerous variations with distinct characteristics that
make them suitable for different applications.
FIGURE1: RUBBERS
PROCEDURE:
First of all, check the zero error in the dial indicator for the sake of accurate result.
Set the dial indicator at zero.
With the hanger in position apply a load to the hanger and read the vertical displacement
of the loading plate relative to the fixing plate from the dial indicator.
Repeat the experiment for increasing load and record the vertical displacement of the
loading plate in each case.
Unload and not the corresponding reading with the load decreasing
Calculate the modulus of rigidity of the rubber material.
OBSERVATIONS AND CALCULATIONS:
Length of rubber block (l) = 11.88 in
Width of rubber block (w) = 4.01 in
Thickness of rubber block (t) = 0.98 in
Least count of dial indicator = 0.0004 in
LAB SESSION 5
To determine the central deflection of a simply fixed ended beam loaded by a
concentrated load at mid-point and compare the experimental and theoretical values.
OBJECTIVES:
Determine the deflection of the beam
Observing the central deflection of a simply supported beam
To draw the load deflection graph
APPARATUS:
Deflection of beam apparatus
Weights
Hangers
Vernier Caliper
Wei
Steel Rule ghts
APPARATUS DIAGRAM:
GaugeFigure 2:
Fixed Ended Beam
LAB SESSION 6
To investigate modulus of elasticity of cantilever beam subjected to
concentrated loading at midspan.
OBJECTIVES:
Measure the deflection of a cantilever beam under the load
To compare theoretical and experimental values.
APPARATUS:
Propped cantilever beam apparatus
Weights
Dial gauge
Vernier caliper
Hangers
Specimen
Spanner
APPARATUS DIAGRAM:
Figure1: apparatus diagram
THEORETICAL BACKGROUND:
Beam:
A beam is a structural element that primarily resists loads applied laterally to the beam's axis
(an element designed to carry primarily axial load would be a strut or column). Its mode
of deflection is primarily by bending. The loads applied to the beam result in reaction
forces at the beam's support points. The total effect of all the
forces acting on the beam is to produce shear
forces and bending moments within the beams, that in turn
induce internal stresses, strains and deflections of the beam.
Beams are characterized by their manner of support, profile
(shape of cross-section), equilibrium conditions, length, and
their material [1].
figure3:beam
TYPES OF BEAMS:
There are several types of beams. Here are some common types of beams:
Simply Supported Beam
Cantilever Beam
Continuous Beam
I-Beam (or H-Beam)
Cantilever Beam: A cantilever is a rigid structural element that extends horizontally and
is supported at only 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.
When subjected to a structural load at its far, unsupported end, the cantilever carries the load
to the support where it applies a shear stress and a bending moment.[2]
Application of cantilever beam:
In Buildings.
Cantilever bridges.
Overhanging projections and elements.
Balconies such as in Frank Lloyd Wright’s Falling Water.
Machinery and plants such as cranes.
Overhanging roofs like shelters and stadium roofs.
Shelving and Furniture.[3]
figure4: cantilever beam
Advantages of cantilever beam: [4]
1. In construction, these beams are simple.
2. On the opposite side, it does not require support.
3. This beam generates a negative bending moment which counteracts the positive bending
moment of back spans.
4. Because of the beam added to the cantilever arms, the span can be greater than that of a
simple beam.
5. Thermal expansion and ground movement are reasonably simple to sustain because the
beam is resting simply on the arms.
6. Due to their depth, cantilever beams are very rigid.[5]
PROCEDURE:
1. Set the deflection of the beam apparatus on a horizontal surface.
2. Set the dial indicator to zero.
3. Apply the load of 0.5lb and measure the deflection using dial indicator.
4. Take the set of at least five readings of increasing value of load and then take readings on
unloading.
5. Calculate:
a. The ‘theoretical value of deflection(yc)’ of the beam at mid-span.
b. The %age error between the theoretical and experimental values of central
deflection.
OBSERVATION AND CALCULATION:
Least Count of the dial indicator = 0.0004 in
Effective length of beam (L) = 20.8 in
Breadth of beam (b) = 1 in
Height of beam (h) = 0.24 in
Modulus of elasticity of material of the beam (SILVER) = 1.2×107psi
