# The rigid bar AC is supported by two axial bars

1. Feb 23, 2015

### Triathlete

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

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

3. 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

2. Feb 24, 2015

### paisiello2

When you took moments about point A, what was your sign convention?

3. Feb 24, 2015

### Triathlete

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.

4. Feb 24, 2015

### paisiello2

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: Feb 24, 2015
5. Feb 25, 2015

### Triathlete

Yeah I re did my calculations and it turns out I wrote down the wrong number .
I solved it, thanks for your help!