Thin and Thick Cylinders

Advanced Structural Analysis

EGF316

Lecture Content

• Thin cylinders under pressure

• Hoop stress

• Longitudinal stress

• Strains and changes in dimension

• Thick cylinders under pressure

• Lamé’s theory

• Longitudinal stress

• Maximum shear stress

• Strains and changes in dimension

Some typical examples

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Some failures in history

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Stresses in cylinders

Stresses in cylinders

– cylindrical coordinates

Thin Vs Thick Cylinders

Thin Cylinders Thick Cylinders

Di

t

all are constant

is negligible

is constant

vary with radius

Thin Cylinder – hoop stresses

Thin Cylinder - longitudinal stress

Changes in Dimensions

Change in length:

Change in diameter:

Change in volume:

Example 1:

Example 2:

Thick Cylinders - Lamé’s Theory

Lamé’s Theory

Lamé’s Theory

Internal Pressure Only

Longitudinal Stress

Maximum Shear Stress

Strains

Changes in Dimensions

Change in diameter:

Change in length:

Change in volume:

Example 3:

A tube has 100mm inner diameter and the walls are

20mm thick. It is subjected to an internal pressure of

20MPa.

Calculate the maximum error in hoop stress at the

surface if a thin tube criterion based on the inner

diameter is used.

Example 4:

Class Test in next session – 30%

Content – Course material so far

Type – Open book

Duration – 1 hour