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

[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

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 ?

 

[PhanthomJay]

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..."?

 

[foo9008]

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?

 

[foo9008]

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 ?

 

[PhanthomJay]

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

 

[foo9008]

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?

 

[PhanthomJay]

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.