# Question 2.9: A steel pipe of length 6 m, outside diameter 45 mm and wall ......

A steel pipe of length 6 m, outside diameter 45 mm and wall thickness 10 mm as shown in Figure 2.20 is subjected to an axial compressive load of 400 kN. Assuming that E = 200 GPa and poisson’s ratio of 0.3 find: (a) shortening of the pipe, (b) the increase in outside diameter, (c) the increase in wall thickness.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.

The steel pipe is shown in Figure 2.20.
(a) To calculate the shortening of the pipe we make use of the formula:

$\begin{gathered} d l=\frac{P L}{A E}, A=\frac{\pi}{4}\left(45^2-25^2\right)=1099.55 mm ^2 \\ L=6000 mm , E=200 \times 10^3 N / mm ^2 \\ d l=\frac{400 \times 10^3 \times 6000}{1099.55 \times 200 \times 10^3}=10.91 mm \end{gathered}$

(b) Increase in outside diameter

\begin{aligned} \text { Linear strain } & =E_{\text {long }}=\frac{10.91}{6000} \\ & =0.0018 \\ \text { Lateral strain } & =0.3 \times 0.0018 \\ & =0.00054 \end{aligned}

∴      Increase in outside diameter

dd = d × 0.00054
= 45 × 0.00054
= 0.0243 mm

(c) Increase in wall thickness

dt = 10 × 0.00054
= 0.0054 mm

Question: 2.22

## A member ABCD is subjected to point loads P1 = 45 kN, P2 = 100 kN, and P4 = 130 kN. Determine the net elongation of the member. Assume E = 210 GPa. Refer Figure 2.35(a). ...

For the external equilibrium, algebraic sum of hor...
Question: 2.1

## A bar having two different cross sectional areas is loaded by axial force as shown in Figure 2.15. Both parts of the bar have circular cross section. The diameter of parts AB and BC are 40 mm and 25 mm respectively. Calculate normal stresses in portion AB and BC of the bar. ...

As it is clear from Figure 2.15 that the portions ...
Question: 2.2

## A hollow pipe of inside diameter 40 mm and outside diameter 50 mm is compressed by an axial force of 55 kN. Calculate compressive stress in the material of the pipe. ...

This problem is also straightforward as the previo...
Question: 2.3

## A horizontal bar CBD having length of 2.4 m is supported and loaded as shown in Figure 2.17. The vertical member AB has cross sectional area of 550 mm². Determine the magnitude of load P so that it produces a normal stress equal to 40 MPa in member AB. ...

The system shown in Figure 2.17 is in equilibrium....
Question: 2.4

## Obtain an expression for change in length of a freely hanging wire of diameter d and length l. Unit weight of the material of the wire is w. ...

We know that the change in length of a prismatic c...
Question: 2.5

## A strut and cable assembly ABC supports a vertical load as shown in Figure 2.18(a). The cable has an effective area of cross section 120 mm², and the strut has an area of 250 mm². Calculate the normal stresses in cable and strut and indicate the nature of stresses. If the cable elongates 1.3 mm, ...

The assembly is in equilibrium. The free-body diag...
Question: 2.7

## A compression member constructed from steel pipe has an outside diameter of 90 mm and a cross sectional area of 1580 mm². What axial force P will cause the outside diameter to increase by 0.0094 mm? Given E = 200 GPa and 1/m = 0.3. ...

First, we shall calculate longitudinal strain [lat...
Question: 2.6

## A tensile test is performed on a brass specimen 10 mm in diameter using a gauge length of 50 mm. When applying axial tensile load of 25 kN, it was observed that the distance between the gauge marks increase by 0.152 mm, calculate modulus of elasticity of brass. ...

The problem is sketched in Figure 2.19. Modulus of...
Question: 2.10