Reaction at support and internal axial force resultant

Consider two straight bars of uniform cross section made of the same material. Bar 1 has an axial length 1m of and a square cross section 1mm with side length . Bar 2 has an axial length of 3 m and a round cross section with 2mm diameter. When subjected to 1KN 2 axial tension, bar 1 elongates by 5mm . What will be the elongation of bar 2, , if it is compressed axially with a load of 25KN ?

-119.36mm

Mukesh, could you please explain how?

To find the elongation of bar 2 when compressed with a load of 25KN, we need to calculate the internal axial force resultant in bar 2.

First, let's find the internal axial force resultant in bar 1 when it is subjected to an axial tension of 1KN.

The internal axial force resultant can be calculated using the formula:

F = E * A * ΔL / L

Where:
F is the internal axial force resultant,
E is the Young's modulus (which can be assumed to be the same for both bars, given that they are made of the same material),
A is the cross-sectional area of the bar,
ΔL is the elongation or compression in the bar,
L is the original axial length of the bar.

For bar 1:
The axial length, L, is given as 1m.
The cross-sectional area, A, is (1mm)^2 = 1mm^2 = 0.001mm^2 = 0.001 × 10^-6 m^2.

From the given data, ΔL for bar 1 is 5mm = 5 × 10^-3 m.

Now, we can calculate the internal axial force resultant using the formula:

F1 = E * A * ΔL1 / L1

Next, let's find the internal axial force resultant in bar 2 when it is compressed with a load of 25KN.

For bar 2:
The axial length, L2, is given as 3m.
The cross-sectional area, A2, is πr^2, where r is the radius of the cross-section. The radius can be calculated using the diameter given as 2mm, which is equal to 2 × 10^-3 m. So, r = 1 × 10^-3 m.

From the given data, we have the load applied, F2 = 25KN.

Now, we can calculate the elongation in bar 2 using the formula:

ΔL2 = F2 * L2 / (E * A2)

Finally, substitute the values into the equation to find the elongation of bar 2:

ΔL2 = (25 × 10^3) * 3 / (E * π * (1 × 10^-3)^2)

Please note that the final value of ΔL2 will depend on the value of E, the Young's modulus, which needs to be known.