NANYANG TECHNOLOGICAL UNIVERSITY

First Year Engineering Course

FE1073: An Introduction to Engineering and Practices

Laboratory Manual

For

Experiment C2

Deformation of Elastic Body

Laboratory: Protective Engineering

Location: N1.1 - B5 - 02

School of Civil andEnvironmental Engineering

[CEE]

Session 2013 / 2014

FE1073-C2

DEFORMATION OF ELASTIC BODY

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

Deformation of elastic body

1. OBJECTIVE

To measure the deformation (strain) in a truss member and determine the modulus of elasticity of the material involved. Also determine the stiffness of the rigid body.

2. THEORY

As shown in Figure 1, the system is consisted of a truss member BG and a rigid body OB, which are joined together at their end. The system has pin-joints at O, B and G. The member OB is very rigid when compared with BG. Therefore, deformations in OB are 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 this rigid body as an objective (Figure 2), with one of the equilibrium condition of elastic body, as following Equation (1).

P

H

L1

L

L0

O B

G

D

2

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Figure 2 The force model of the rigid body OB

(1)

Then we can obtain the unknown force FBG, and the stress (force per unit area) in member BG with given the cross-sectional area A.

(2)

(3)

If the force for FBG is in Newton (N) and the unit for length is in millimeter (mm), the stress will be in N/mm2 or mega Pascal (MPa, 1Pa = 1 N/m2)

Most engineering structures are designed to function within the linear elastic range, i.e., the stress is linearly proportional to the strain,

(4)

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.

For member BG, substitute (3) into (4) and arrange, we have

(5)

Another quantity which is of interest in this case is the deflection p at point D where force P is applied. When the deformations in OB can be neglected, B will move to B due to the deflection at point B and extension BG in member BG. The rotation between BG and B’G is very small and we can consider that GC=GB’ (see Figure 8). Therefore, we can see there is a compatible relationship between and BG, as shown in Equation (6). One

P

FBG

Fox

Foy

FBGsinθ

FBGcosθOBD

L1

L

3

FE1073-C2

more relationship implied is the vertical deflection at point D and B of member OB (Equation 6).

Figure 3 Deformation formats for this system (the deformation is exaggerated and just for illustration)

(6)

Define a stiffness coefficient, k, which means the force needed if there is a unit deflection at point D, as

(7)

By plotting the relationship between and the measured strain 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).

3. EQUIPMENT

Truss model, Weights, Strain monitoring equipment, Calipers and Ruler.

Materials Student needs to bring the following items:

a) 30cm Rulerb) A4 graph papers (4 sheets)c) A4 Writing Pad

4. EXPERIMENT

To measure all the necessary dimensions and then record strain increments while loading and unloading. Conduct the experiment for two cases: (1) apply load P at point B; and (2) apply load P at point D. Important note:

OB

G

B'

BG

L0

L

p

C

D

L1

4

FE1073-C2

(i) The cross-sectional dimensions must be measured at three different locations along the member and the average cross-sectional area should be used for computations.

(ii) Loading steps must be as indicated on the data sheets.

(ii) Strain = strain increment x conversion factor (CF)

5. REPORT PART

Data processing and calculations

(Accuracy up to three significant digits required; “three significant digits” and “three decimal places” have different meanings)

(i) Complete the data sheet and attach it to the report.

(ii) Plot the stress versus strain increment for the truss model.

(iii) Using the slope of the plot, determine the Young’s modulus (in kN/mm2) of the material used for the inclined member and the stiffness k at the point of force applied.

Discussion

Answer the following questions:

(i) What is the significance of observed strains fitting in to a straight line in the plot of vs ?

(ii) If member BG is replaced by another member of same length but different cross-section, will the tensile force FBG be different under the same load P (assuming small deformations anyway)? What about the deflection at point D? Give reasons.

Further Discussion for the Formal Report

(i) Discuss qualitatively how the rigidity of member OB affects the results of the experiment?

(ii) Why is it preferable to measure the strain along GB rather than the deflections with a dial gauge mounted on the truss at B?

Conclusions

Keeping the objectives of the experiment in mind to conclude your findings.

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FE1073-C2

Experiment C2: Deformation of Elastic Body

DATA SHEET

Name: Date:

Group No.: Lecturer:

Table 1: Test Results of Truss Model

Cross-sectional Parameter

b(mm) t(mm) Area(mm2)

1

2

3

Average Area = __________mm2

Other Relative Dimension

L0 (mm) H (mm)

Experiment C2: Deformation of Elastic BodyDATA SHEET

6

FE1073-C2

Case 1

The force P applied at the joint B ( )

Conversion factor for strains CF = 0.5 (to be confirmed by the instructor)

P (N) FBG (N) (MPa)

Strain Increment

Loading Unloading

0

10

20

30

40

50

60

Elastic Modulus (slope based on the graph) E = (kN/mm2)

Stiffness k = (kN/mm)

(DO NOT show any calculation on the data sheet. Show the calculations neatly on a separate sheet)

Experiment C2: Deformation of Elastic BodyDATA SHEET

7

FE1073-C2

Case 2

The force P applied at the midpoint (D) of OB ( )

Conversion factor for strains CF = 0.5 (to be confirmed by the instructor)

P (N) FBG (N) (MPa)

Strain Increment

Loading Unloading

0

10

20

30

40

50

60

Elastic Modulus (slope based on the graph) E = (kN/mm2)

Stiffness k = (kN/mm)

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