# Deformation Of Elastic Body C2 Lab Report

Topics: Young's modulus, Elasticity, Elastic modulus Pages: 14 (1858 words) Published: October 29, 2014
1. ABSTRACT

In this experiment, we will measure the stress and the strain in an elastic body, observe Hooke's law and determine the modulus of elasticity of the material. Furthermore, the stiffness k of the rigid body is determined as well. 2. OBJECTIVE

To measure the deformation (strain) in a truss member, determine the modulus of elasticity of the material involved and the stiffness of the rigid body. 3. THEORY
As shown in figure one, the system consists of a truss member BG and a rigid body OB, which are joined together at their ends. The system has pin-joints at O, B and G. The member OB is very rigid when compared with BG. Therefore, any deformation in OB is neglected and OB is treated as a rigid body.

Figure 1 Experiment setup
Each truss member acts as a two-force member. If the force tends to elongate the member, it is a tensile force (T); whereas if it tends to shorten the member, it is a compressive force (C). Take the rigid body OB as an object shown in Figure 2. One of the equilibrium conditions for this elastic rigid body is given by Equation (1).

Formal Report: Deformation of Elastic Body

Page 1

Figure 2 The force model of the rigid body OB

With a given applied force P, we can then obtain the unknown force, FBG, and the stress (force per unit area) in member BG with given cross sectional area, A.

If the force for FBG is in Newton (N) and the unit for length is in millimeter (mm), the stress will be in N/mm or Mega Pascal (MPa, 1Pa = 1 N/m). Most engineering structures are designed to function within the linear elastic range, i.e., the stress σ is linearly proportional to the strain ε,

This relation is known as Hooke’s law. The coefficient E is called the modulus of elasticity (or also Young’s modulus) of the material involved.

Formal Report: Deformation of Elastic Body

Page 2

Figure 2 The force model of the rigid body OB

With a given applied force P, we can then obtain the unknown force, FBG, and the stress (force per unit area) in member BG with given cross sectional area, A.

If the force for FBG is in Newton (N) and the unit for length is in millimeter (mm), the stress will be in N/mm or Mega Pascal (MPa, 1Pa = 1 N/m). Most engineering structures are designed to function within the linear elastic range, i.e., the stress σ is linearly proportional to the strain ε,

This relation is known as Hooke’s law. The coefficient E is called the modulus of elasticity (or also Young’s modulus) of the material involved.

Formal Report: Deformation of Elastic Body

Page 2

Define a stiffness coefficient, k, which is the force needed to introduce a unit deflection at point D, as

By plotting the relationship between σ and the measured strain ε for a range of applied P values, the Young’s modulus E and the stiffness coefficient k can be determined from the experiment using equations (5) and (7).

4. EQUIPMENT

Truss model

Weights

Strain monitoring equipment

Calipers

Ruler

5. EXPERIMENTAL PROCEDURES
For case 1
1. Measure and record the cross-sectional dimensions at three different locations along the member BG. Calculate the average cross-sectional area of the member. 2. Load the truss at point B in the order of 0N, 10N, 20N, 30N, 40N, 50N, 60N, record the respective ε’ values.

3. Unload the truss from 60N to 10N, decreasing the load by 10N each time and record the respective ε’ values.
4. Calculate the strain ε, whereby ε = ε’ x conversion factor (CF). 5. Plot stress σ against strain increment  for the truss model. 6. Using the slope of the plots, we obtain the modulus of elasticity, E , of the material involved and using equations 5 and 7 we can determine the stiffness coefficient k.

Formal Report: Deformation of Elastic Body

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For case 2:

Repeat steps 2 to 7 of the experiment conducted in case 1, changing the point of loading and unloading to point D on the truss.

6. RESULTS

Table 1: Test...

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