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A circular bar is subjected to an axial pull of 100kN.if the maximum intensity of shear stress on any plane is not to exceed 60MN/m^2 determine the diameter of the bar.

I know the answer to this is 32.6mm, what I need to know is how to arrive at this number so that I know how to do it.

Respuesta :

mathmate
Use a Mohr circle to find the maximum shear stress relative to the axial stress.
Here we assume the axial stress is sigma, the transverse axial stress is zero.
So we have a Mohr circle with (0,0) and (0,sigma) as a diameter.
The centre of the circle is therefore (0,sigma/2), and the radius is sigma/2.
From the circle, we determine that the maximum stress is the maximum y-axis values, namely +/- sigma/2, at locations (sigma/2, sigma/2), and (sigma/2, -sigma/2).
Given that the maximum shear stress is 60 MPa, we have
sigma/2=60 MPa, or sigma=120 MPa.
(note: 1 MPa = 1N/mm^2)
Therefore
100 kN/(pi*d^2/4)=100,000 N/(pi*d^2/4)=120 MPa  where d is in mm.
Solve for d
d=sqrt(100,000*4/(120*pi))
=32.5735 mm
Lanuel

Based on the calculations, the diameter of this bar is equal to 32.6 millimeters.

Given the following data:

  • Axial pull = 100 kN.
  • Maximum shear stress (σ/2) =60 MN/m².

How to determine diameter of the bar?

In order to determine diameter of this bar, we would use Mohr circle equation to solve for the maximum shear stress with respect to the axial stress.

Let the axial stress be σ and the transverse axial stress be zero (0). Therefore, a Mohr circle with a diameter of (0, 0) and (0, σ) is formed.

Also, the center of this circle would be equal to (0, σ/2) with a radius of σ/2.

Note: σ = 60 × 2 = 120 MPa = 120 N/mm².

From the equation for maximum shear stress, we have:

σ = F/(πd²/4)

Making d the subject of formula, we have:

d = √(4F/σπ)

Substituting the given parameters into the formula, we have;

d = √(4 × 100,000/120 × 3.142)

d = √(400,000/377.04)

d = √1,060.90

d = 32.6 mm.

Read more on maximum shear stress here: https://brainly.com/question/14723964

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