Thin Cylinder

Topics: Force, Elasticity, Solid mechanics Pages: 12 (3169 words) Published: June 22, 2013
MEMB221
MECHANICS AND MATERIALS LABORATORY
SEM 2 2012/13

EXPERIMENT 6: THIN CYLINDER
DATE PERFORMED: 13TH DECEMBER 2012
DUE DATE: 20TH DECEMBER 2012
SECTION: 2
GROUP NUMBER: 6
GROUP MEMBERS:
a) MUHAMAD HADI BIN MOHAMED RADZI (ME087932)
b) THINES A/L MURUGAN(ME086895)
c) MUHAMMAD HASRUL BIN ROSLI (ME087000)
d) HAIZUM AMALINA BINTI A. WAHID (ME087898)
LAB INSTRUCTOR: MADAM NOLIA HARUDIN

TABLE OF CONTENT

No.| Content| Page|
1.| Summary / Abstract| 3|
2.| Statement of Purpose / Introduction / Objectives| 4| 3.| Theory | 4-10|
4.| Equipment / Description of Experimental Apparatus| 11-13| 5.| Procedure| 14-15|
6.| Data and Observations| 16-17|
7.| Analysis and Results * Table * Sample Calculations * Graph| 18-21| 8.| Discussions | 22|
9.| Conclusions | 23|
10.| References | 23|
11.| Appendices| |

SUMMARY/ABSTRACT:
Generally, this experiment is done to find the value of Young Modulus under circumferential condition of stress, principle strains and Poisson’s ratio. Software called SM1007 is introduced in this experiment to help students in finding the value of Young’s Modulus, Poisson’s ratio and principle strains required. The cylinder in open ends condition has no end constraint and therefore the longitudinal component of stress will be zero, but there will be some strain in this direction due to the Poisson effect.

In this experiment we discussed the stresses in thin cylinder and derive formulas relating the stresses in the walls of the cylinder and the gage pressure p in the fluid they contain. In the case of a cylindrical vessel of inside radius r and thickness t, we obtained the following expression for the hoop stress H and the longitudinal stress L. Mohr’s circle provides an alternative method, based on simple geometric considerations, for the analysis of the transformation of plane stress.

Thin-walled pressure vessels provide an important application of the analysis of plane stress. Since their walls offer litter resistance to bending, it may be assumed that the internal forces exerted on a given portion of wall are tangent to the surface of the vessel. The resulting stresses on an element of wall will thus be contained in a plane tangent to the surface of the vessel. From the data collected, Poisson’s Ratio can be calculated. Because from the theory axial strain applied to a cylinder, transversal strain will occur. As it is not possible to measure all strains, these have to be computed on the basis of marginal conditions. Initial stress at the surface must zero, longitudinal stress is constant over the radius are the marginal conditions to obtain the solution.

STATEMENT OF PURPOSE/INTRODUCTION/OBJECTIVE:
* To determine the circumferential stress under open condition and analysis of combined and circumferential stress.

THEORY:
a) Complex Stress System
The diagrams in the figure below represent a) the stress and b) the forces acting upon an element of material under the action of two-dimensional stress system.
Assuming b) to be a ‘wedge’ of material of unit depth and the side AB to be of unit length : Resolving along σθ will give :
σθ = 12 (σy + σx) + 12 (σy - σx)cos2θ + τsin2θ …….1

Resolving along τθ will give :
τθ = 12 (σy - σx)sin2θ - τcos2θ ……..2
From equation 2 it can be seen that there are values for e for which τθ is zero and the planes on which the shear component is zero are called ‘Principal Planes’. For equation 2:τ = 12 (σy - σx)tan2θ ……..3

This will give two values of 2θ differing by 180˚ and, therefore, two values of θ differing by 90˚. This shows that Principal Planes are two planes at right angles to each other.

From the diagram above :
sin2θ =±2τ(σy- σx)2+4τ2 ……4
and
cos2θ =±(σy- σx)2(σy- σx)2+4τ2 ……5
The stresses on the principal planes are normal to these planes and are called principal stresses.
From equation 1 and...
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