The rigid bar AC is supported by two axial bars

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Discussion Overview

The discussion revolves around a homework problem involving a rigid bar supported by two axial bars made of bronze. Participants are tasked with determining the magnitude of a load and the vertical displacement of a pin after a temperature increase, using principles of mechanics and material properties.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • The initial approach to solving the problem involved calculating the thermal strain due to temperature change and then determining the stress and force in bar (2) using the equations provided.
  • One participant questioned the sign convention used when taking moments about point A, suggesting that clarity on this aspect is crucial for solving the problem correctly.
  • Another participant pointed out a potential arithmetic mistake in the calculations, indicating that a free body diagram might assist in visualizing the forces and moments involved.
  • A later reply confirmed that the participant had re-evaluated their calculations and found an error, leading to a successful resolution of the problem.

Areas of Agreement / Disagreement

There appears to be no consensus on the initial calculations, as one participant identified a mistake, but the discussion ultimately led to a resolution for the original poster. However, the specific details of the sign convention and its impact on the calculations remain a point of clarification.

Contextual Notes

Limitations include potential errors in arithmetic and the need for a clear understanding of sign conventions in moment calculations. The discussion does not resolve the broader implications of these calculations on the overall problem.

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Homework Statement


The rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; α = 18 × 10−6 mm/mm/°C]. The cross-sectional area of bar (1) is A1= 211 mm2 and the cross-sectional area of bar (2) is A2 = 303 mm2. After load P has been applied and the temperature of the entire assembly has increased by 21°C, the total strain in bar (2) is measured as 1210 με (elongation). Determine:
(a) the magnitude of load P.
(b) the vertical displacement of pin A.

upload_2015-2-23_19-13-16.gif


Homework Equations



εT = αΔT
εσ = εtotal - εT
σ = Eε
σ = F/A

The Attempt at a Solution



I started by using the first equation and getting the strain caused by temp change in bar (2) → (18x10-6)(21) = 0.000378
Then, I plugged that result into the second equation to get strain caused by normal stress in bar (2) → 0.00121 - 0.000378 = 0.00032
I plugged this result into the third equation to get the stress in bar (2) → (0.00032)(100) = 0.032 GPa = 32 MPa
Then I plugged this into the fourth equation to solve for the force F2 → (32 N/mm2)(303 mm2) = 6752 N

To find P, I used the moment about point A → -480P - (9696)(1210) = 0 ⇒ P = 24442 N = 24.4 kN

My answer was incorrect, and I really have no idea what to do.

As for part b), I'm not really sure where to begin.
Any help would be appreciated, I really struggle at FBD's and correctly labelling moments and forces so if I could see one for this problem it would be a big help :smile:
 
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When you took moments about point A, what was your sign convention?
 
paisiello2 said:
When you took moments about point A, what was your sign convention?

I took ccw as negative and cw as positive. Moments are not my forte so I'm pretty sure I'm doing something wrong here.
 
OK, can you explain then how you determined the signs in your last equation? A free body diagram might help as well.

I think you made a simple arithmetic mistake in step 4 but seem to have corrected for it in the last equation.

Check your arithmetic in the 2nd step.
 
Last edited:
Yeah I re did my calculations and it turns out I wrote down the wrong number o0).
I solved it, thanks for your help!
 

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