Statics Lab

Topics: Young's modulus, Elasticity, Solid mechanics Pages: 6 (1209 words) Published: July 2, 2014
UNIVERSITI TUNKU ABDUL RAHMAN
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Engineering & Science
ME, MM, MH, BI, CI, CL
Y1S1, Y1S2, Y1S3

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Unit Code
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UEME1132
Statics
Ms. Lam Foong Sin

201405

Experiment 1: Young’s Modulus
Introduction
The Young’s Modulus Apparatus is a bench-top model designed for students to understand and to determine Young’s Modulus of given material samples.
It consists of an epoxy coated steel reaction frame complete with a meter long linear scale. Two adjustable supports provide the variable span needed to perform the experiment. Stainless steel weights and hangers are provided for applying loading to the beams. One set of dial gauges to 0.01 mm resolution, complete with mounting brackets are employed for the measurement of the beam deflection.

A theory and experiment Work Sheet is provided for students to follow the appropriate procedure of operation and computation.
Experimental Capabilities
1. To investigate the relationship between load, span width, height (depth) and deflection of a simply supported beam.
2. To ascertain the Coefficient of Elasticity (Young’s Modulus) for steel, brass and aluminium. Accessories : Set of Stainless steel hanger and weights
Set of dial gauges (0.01 mm resolution)
Four leveling feet with built-in spirit level
Dimensions : 1050 x 400 x 300 mm
Weight : Approximately 50kg
Young’s Modulus
The elastic modulus is one of the most important properties involved in various aspects of material engineering for design purposes. Every material undergoes elastic deformation under actions. Elastic deformation is mostly defined as temporary deformation of its physical shape and will be able to return to its original state upon removal of actions. For elastic deformation, the stress state of the material had not exceeded its elastic limit. Any deformation caused by further increases in load or stress beyond the yield point of a certain material will cause plastic deformation (permanent or non-recoverable).

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The Young’s modulus (elastic modulus) is a measurement of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. Besides using the stress and strain graphs, the Young’s modulus of any material can also be determined by using the deflection of the material (beam) when subjected to load.

The deflection of a beam depends on its length, its cross-sectional shape, the material, where the deflecting force is applied, and how the beam is supported.
Moment of Inertia, I
Moment of Inertia, I, is the property of an object associated with its resistance to rotation. It depends on the mass of an object and the distribution of mass with respect to the axis of rotation. For a prismatic beam, the Moment of Inertia at a section is calculated based on the cross-sectional shape and the thickness (depth). For a rectangular section beam, I = bh3/12.

Moment of Inertia for rectangular section
I = bh3/12 ……… b = width of beam
h = height of beam

Moment of Inertia for circular section
I = ʌd /64 ……… d = diameter of the circular section
r = radius of the circular section
I= πr4/4
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Deflection equation with different beam support types
1. One fixed end and one simple support end

F = load (action) applied
L = beam length
a= intermediate length of beam
į = deflection
E = Young’s Modulus
I = Moment of inertia
The deflection at length a from the fixed support is:
į = Fa3(L - a)2(4L - a) / 12EIL3
For a load in the centre of the beam, substituting a = L/2 in the above equation, the deflection is: į = 3.5FL3 / 384EI
2. Two simple supports end

The deflection at distance a from the left-hand support is:
į = Fa2(L - a)2/3EIL
For a load in the centre of the beam, substituting a = L/2 in the above equation, the deflection is: į = FL3/48EI

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EXPERIMENTS
BENDING OF BEAM AND COEFFICIENT OF ELASTICITY
Objective
Part 1: To...

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