# What is the Minimum Width of a Structural Steel Bar with Applied Axial Forces?

• foo9008
In summary, the problem involves determining the minimum width, w, of a structural steel bar with 40mm diameter and 25mm thickness subjected to 4 axial forces. The maximum allowable tensile stress in the bar is 135MPa and the maximum allowable deformation is 1.25mm. Using the equation δ = PL/AE, where δ is deformation, P is force, L is length, A is area, and E is modulus of elasticity, a minimum width of 65.2mm is required to ensure that no point in the bar is stressed beyond the maximum allowed stress. The stress in the left and mid sections of the bar will be less, as the right section with the higher load, and hence higher stress
foo9008

## Homework Statement

There are 4 axial forces that are applied to 25mm thick structural steel bar with 40mm diameter . If the maximum allowable tensile stress in the bar is 135MPa and the maximum allowable deformation (extension or contraction) of bar is 1.25mm , determine the minimum width , w of the bar , E = 200GPa

## The Attempt at a Solution

i have divided the bar into 3 sections , namely AB , BC and also CD. For part AB, the force acting on it 90kN tensile force , for BC , the force acting on it is 50kN compressive force , for CD, the force acting is 220kN tensile force. )We know that δ(defomation ) = PL / AE , where P - force , L = length of bar , A = area

so i let 1.25x10^-3 = ((90x10^3)(250x10^-3) - (50x10^3)(500x10^-3) + (220x10^3)(750x10^-3) / (25x10^-3 x w x 200x10^9) , so w = 26mm ,

but the ans given is w = 65 mm , which part of my working is wrong ?

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foo9008 said:

## Homework Statement

There are 4 axial forces that are applied to 25mm thick structural steel bar with 40mm diameter . If the maximum allowable tensile stress in the bar is 135MPa and the maximum allowable deformation (extension or contraction) of bar is 1.25mm , determine the minimum width , w of the bar , E = 200GPa

## The Attempt at a Solution

i have divided the bar into 3 sections , namely AB , BC and also CD. For part AB, the force acting on it 90kN tensile force , for BC , the force acting on it is 50kN compressive force , for CD, the force acting is 220kN tensile force. )We know that δ(defomation ) = PL / AE , where P - force , L = length of bar , A = area

so i let 1.25x10^-3 = ((90x10^3)(250x10^-3) - (50x10^3)(500x10^-3) + (220x10^3)(750x10^-3) / (25x10^-3 x w x 200x10^9) , so w = 26mm ,

but the ans given is w = 65 mm , which part of my working is wrong ?
Deformation analysis looks good, but did you check this wording from the problem statement "... the maximum allowable tensile stress in the bar is 135MPa..."?

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foo9008
PhanthomJay said:
Deformation analysis looks good, but did you check this wording from the problem statement "... the maximum allowable tensile stress in the bar is 135MPa..."?
So how should I proceed?

ok , when using force = 220kPa , i found that w = 65.2mm, but when i use P = 50kN , w = 14.8mm , when using P = 90kPa , my t = 24mm , why is it so ?

if so , then it's maximum t , right ?

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yes, since the bar is uniform in dimensions, the higher number controls for stress.

PhanthomJay said:
yes, since the bar is uniform in dimensions, the higher number controls for stress.
Just to double check, the 65.2mm is the maximum t, not minimum t, am I right?

foo9008 said:
Just to double check, the 65.2mm is the maximum t, not minimum t, am I right?
I may not have responded clearly. The 65 mm thickness is the minimum t required such that no point in the bar is stressed beyond the max allowed stress of 135 MPa. The stress in the left and mid sections will be less, as the right section with the higher load, and hence higher stress, controls the design.

foo9008

## What is the width of a bar?

The width of a bar is the measurement of how wide the bar is from one side to the other. It is usually measured in units such as inches, centimeters, or pixels.

## How do you find the width of a bar?

To find the width of a bar, you can use a ruler or measuring tape to physically measure the bar's width. Alternatively, if you have a digital image or diagram of the bar, you can use software tools to measure its width.

## Why is it important to know the width of a bar?

The width of a bar is important because it can provide information about the bar's strength and stability. It can also be used to calculate the volume or area of the bar, which may be necessary for certain applications or experiments.

## What are some common methods for measuring the width of a bar?

Some common methods for measuring the width of a bar include using a ruler, measuring tape, caliper, or specialized tools such as a micrometer or laser measurement device. Digital images or diagrams of the bar can also be measured using software tools.

## Can the width of a bar vary?

Yes, the width of a bar can vary depending on the material it is made of, its manufacturing process, and its intended use. It is important to measure the width of a specific bar to ensure accuracy in calculations and applications.