A mild steel bar of width 10mm is subjected to a tensile stress of 3,0x105 Pa. Given that Young’s modulus for mild steel is 200 GPa and Poisson’s ration for mild steel is 0.31, calculate the change in width of the bar. Is the width increased or reduced?

Question

A mild steel bar of width 10mm is subjected to a tensile stress of 3,0x105 Pa. Given that Young’s modulus for mild steel is 200 GPa and Poisson’s ration for mild steel is 0.31, calculate the change in width of the bar. Is the width increased or reduced?

Answer 1

I suggest you review the definition of Poisson's ratio at

http://www.engineeringtoolbox.com/poissons-ratio-d_1224.html

It is the ratio of the transverse strain to the longitudinal strain, with a minus sign stuck on. If a material gets stretched in uniaxial tension, it simultaneously gets thinner in the two perpendicular directions.

In your case, the strain along the direction of the applied tensile force is
dL/L = Stress/E = 3*10^5/200*10^9
= 1.6^10^-6

For mild steel, the dimensionless strain contraction in width is 0.31 times that number, or 4.65*10^-7.
That gets multiplied by 10 mm for the actual width reduction: 4.65*10^-6 mm

Answer 2

To calculate the change in width of the mild steel bar, we can use the formula for Poisson's ratio:

∆W/W = -ν(∆L/L)

Where:
∆W = change in width
W = initial width (10mm)
ν = Poisson's ratio (0.31)
∆L = change in length
L = initial length (unknown)

To find ∆L, we can use the formula for Young's modulus:

σ = E(∆L/L)

Where:
σ = tensile stress (3.0x10^5 Pa)
E = Young's modulus (200 GPa = 200x10^9 Pa)
∆L = change in length
L = initial length (unknown)

Rearranging the formula for ∆L:

∆L = (σL)/E

Substituting the values:

∆L = (3.0x10^5 Pa * L) / (200x10^9 Pa)

Simplifying:

∆L = (3/2) x L x 10^-4

Now we can substitute ∆L into the formula for ∆W/W:

∆W/W = -ν(∆L/L)
∆W = -νW(∆L/L)
∆W = -0.31 x 10mm x ((3/2) x L x 10^-4) / L

Simplifying:

∆W = -0.015 x L x 10^-4

Now we can evaluate the change in width (∆W):

∆W = -0.015 x 10^-4 x L

Since L is unknown, we cannot determine the exact change in width (∆W). However, we can determine whether the width is increased or reduced by looking at the sign of ∆W. Since ∆W is negative, it means the width is reduced.

Answer 3

To calculate the change in width of the bar, we need to use the formula:

Δw = υ * (σ / E) * L

Where:
Δw = Change in width of the bar
υ = Poisson's ratio
σ = Tensile stress
E = Young's modulus
L = Original length of the bar

Given:
υ = 0.31
σ = 3.0 x 10^5 Pa
E = 200 GPa = 200 x 10^9 Pa
L = Not given

Since the length of the bar is not provided, we cannot directly calculate the change in width using the formula. However, we can determine whether the width will increase or reduce by examining the relationship between Poisson's ratio and the sign of the change.

In general, when a material is subjected to tensile stress, it tends to elongate in the direction of the applied force (length increases) and contract in the perpendicular direction (width decreases). The extent of the change in width depends on Poisson's ratio.

For mild steel, with a Poisson's ratio of 0.31, the width tends to decrease when subjected to tensile stress. So, based on the given information, we can conclude that the width of the bar is reduced.

To determine the exact change in width, we would need to know the original length of the bar (L).