# EXPERIMENT 6 MOM

COLLEGE OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

MEMB221 - MECHANICS & MATERIALS LAB

Experiment title : Thin cylinder

Group members: : 1) AHMAD ARIF BIN ZAKARIAME093233

2) KAVIRAJ A/L THIAGARAJANME088972

3) UDHAYA SHARWIN ME088983

Section: 4

Group: 5

Lecturer: PUAN SITI ZUBAIDAH BTE OTHMAN

Performed Date

Due Date

Submitted Date

25/06/2012

09/07/2012

09/07/2012

Table of Content

1.0 Summary/Abstract……………..………………………………………………………...2 2.0 Objective………………………………………………………………………………....3 3.0 Theory……………………………………………………………………………………4 4.0 Equipment……………………………………………………………………………….7 5.0 Procedure………………………………………………………………………………10 6.0 Data and Observations…………………………………………………………………11 7.0 Analysis and Results…………………………………………………………………...16 8.0 Discussion……………………………………………………………………………...18 9.0 Conclusions…………………………………………………………………………….20 10.0 References……………………………………………………………………………..21 11.0 Appendices…………………………………………………………………………….22

1.0 Summary/Abstract

To examine the stress and strain in a thin walled cylinder, students conduct the experiment by using thin cylinder apparatus (SM1007). The experiment clearly shows the principles, theories and analytical techniques and does help the student in studies.

By using SM1007, student will be able to measure the strains of the cylinder in 2 ends condition. Open ends and closed ends. The difference between opened ends and closed ends is that, open ends does not have axial load and no direct axial stress, meanwhile in a closed ends there is axial load and axial stress.

As the result of the experiment, the value of circumferential stress both under open condition and closed condition has been obtained. Analysis has been made and so the calculation. From the data collected in opened ends condition the values of Young’s modulus and Poisson’s ratio are calculated.

2.0 Objective

The objective of this experiment is to determine the circumferential stress under open and closed condition and to analyze the combined stress and circumferential stress.

3.0 Theory

Because this is a thin cylinder, i.e. the ratio of wall thickness to internal diameter is less than about 1/20, the value of σH and σL may be assumed reasonably constant over the area, i.e. throughout the wall thickness, and in all subsequent theory the radial stress, which is small, will be ignored. I symmetry the two principal stresses will be circumferential (hoop) and longitudinal and these, from elementary theory, will be given by: σH = ………… (1)

and

σL = ………… (2)

As previously stated, there are two possible conditions of stress obtainable; 'open end' and the 'closed ends'.

Figure 1: Stresses in a thin walled cylinder

a) Open Ends Condition:

The cylinder in this condition has no end constraint and therefore the longitudinal component of stress σL will be zero, but there will be some strain in this direction due to the Poisson effect. Considering an element of material:

σH will cause strains of:-

εH1 = …………. (3)

and

εL1 = …………. (4)

These are the two principal strains. As can be seen from equation 4, in this condition εL will be negative quantity, i.e. the cylinder in the longitudinal direction will be in compression.

b) Closed Ends Condition :

By constraining the ends, a longitudinal as well as circumferential stress will be imposed upon the cylinder. Considering an element of material: σH will cause strains of:-

εH1 = …………. (5)

and

εL1 = …………. (6)

σL will cause strains of:-

εL = …………. (7)

and

εH = …………. (8)

The principal strains are a combination of these values which are: εH = (σH - ) …………. (9)

εL = (σL - ) …………. (10)

The principal of the strains may be evaluated and the Mohr Strain Circle...

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