Deformation Of Elastic Body C2 Lab Report
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,
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,