Stiffness of Materials Lab Report: Theory, Experiment, Results and Analysis

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ABSTRACT
This report aims at discussing the results obtained from the two experiments. The main findings of the lab
experiment were that the young modulus of the different materials differed despite using the same
measurements and load of materials. The theoretical values vary slightly from the experimental data. The
goal is the support structure is to be optimized for weight and stiffness or deflection. The deflection is
proportional to the load. The stiffness is the slope of the load-deflection curve. Stiffness is experienced in
tension and compression. The deflection in a cantilever beam with two supports on the bottom is
evaluated. The larger the area moment of inertia, the less a structure deflects or the more the stiffness
(Assets press Princeton). The area moment of inertia is an important parameter in determining the state of
stress in a part or component or structure. It is the resistance to buckling and the amount of deflection in a
beam. The area moment of inertia allows you to tell how stiff a structure is. The reference axis in the
beam is the centroidal axis. The deflection is set to be felt on the entire beam as the force is imparted at
the center. The elasticity module is a measure of material deformation under a load. A higher Value of E
implies that the structure deflects slightly (Youssefi and Anagnos).
Key words: Beam, Young’s Modulus, Moment of Inertia, stiffness, tension, compression, Newton law of
motion.
THEORY
Stiffness is a crucial property for many applications of materials. The stiffness of a structure depends on
both the properties of the material from which it is made and on the geometry of the structure. The
deflection of a simply supported beam,
The formula below applies to beams which are subjected to a central load acting at a right angle to their
length. The equation for the deflection of a beam supported between two points is given by:
∆= W L3
48 K
Where w is the load (N), Δ is deflection (m), L is the length (m), K is the flexural rigidity constant. K may
be calculated due to the second moment of area of the material, I, and the value of the Young’s Modulus
E.
K=E . I

Some of the theoretical standard values for materials:
Brass 105 Gpa
Aluminium 69 Gpa
Mild Steel 200 Gpa
The second moments of area (I) for solid and hollow beams is obtained as shown in the equation below.
For a solid beam of rectangular cross section:
I = b d3
12 [ m4 ]
LAB EXPERIMENT
EXPERIMENT 1: EAT103 – STIFFNESS OF MATERIALS
 To achieve an understanding of the stiffness of different materials under load.
The apparatus ES4 uses an example of a very simple structure. It is comprised of a beam in three-point
bending. The apparatus explores beams of different material but identical dimensions and deflects by
different amounts for the same load, providing that their material property affects deflection. The
apparatus used is as illustrated below,