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

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Discussion Overview

The discussion revolves around determining the minimum width of a structural steel bar subjected to multiple axial forces, considering factors such as allowable tensile stress and deformation. Participants explore the implications of their calculations and the conditions under which the minimum width is derived.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a calculation leading to a width of 26mm based on deformation analysis but questions the discrepancy with a provided answer of 65mm.
  • Another participant suggests reviewing the wording of the problem statement regarding the maximum allowable tensile stress to clarify the approach.
  • Further calculations by a participant yield varying widths (65.2mm, 14.8mm, 24mm) based on different applied forces, raising questions about which value should be considered for design.
  • Some participants assert that the higher calculated width controls for stress due to uniform dimensions of the bar.
  • Clarification is sought on whether the calculated width of 65.2mm represents a maximum or minimum requirement, with a later reply indicating it is the minimum thickness needed to avoid exceeding the maximum stress limit.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and interpretations of the problem, with no consensus reached on the correct minimum width. The discussion remains unresolved regarding the implications of the various calculated widths.

Contextual Notes

Participants note potential limitations in their calculations, including assumptions about uniformity and the dependence on specific applied forces. The relationship between stress and width is also highlighted as a critical factor in the design considerations.

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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

Homework Equations

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

Homework Equations

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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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.
 
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