## OIQ-Exam-Question-1 (Version 2)
Technical exam question from Ordre des ingénieurs du Québec.  Obviously meant to be done using moment-distribution, but even easier using slope-deflection.  This version use a newer 'sdutil' that also computes end shears.


```python
from sympy import *
init_printing(use_latex='mathjax')
from IPython import display
```


```python
display.SVG('oiq-exam-1.svg')
```




    

    




```python
from sdutil2 import SD, FEF
var('EI theta_a theta_b theta_c theta_d')
Mab,Mba,Vab,Vba = SD(6,EI,theta_a,theta_b) + FEF.p(6,180,4)
Mbc,Mcb,Vbc,Vcb = SD(8,2*EI,theta_b,theta_c) + FEF.udl(8,45)
Mcd,Mdc,Vcd,Vdc = SD(6,EI,theta_c,theta_d)
```


```python
Mab
```




$$\frac{EI}{6} \left(4 \theta_{a} + 2 \theta_{b}\right) - 80.0$$



Solve equilbrium equations for rotations:


```python
soln = solve( [Mab,Mba+Mbc,Mcb+Mcd,Mdc],[theta_a,theta_b,theta_c,theta_d] )
soln
```




$$\left \{ \theta_{a} : \frac{75.0}{EI}, \quad \theta_{b} : \frac{90.0}{EI}, \quad \theta_{c} : - \frac{190.0}{EI}, \quad \theta_{d} : \frac{95.0}{EI}\right \}$$



Member end moments:


```python
[m.subs(soln) for m in [Mab,Mba,Mbc,Mcb,Mcd,Mdc]]
```




$$\left [ 0, \quad 245.0, \quad -245.0, \quad 95.0, \quad -95.0, \quad 0\right ]$$



Member end shears:


```python
[v.subs(soln).n(4) for v in [Vab,Vba,Vbc,Vcb,Vcd,Vdc]]
```




$$\left [ 19.17, \quad -160.8, \quad 198.8, \quad -161.3, \quad 15.83, \quad 15.83\right ]$$



Reactions:


```python
Ra = Vab
Rb = Vbc - Vba
Rc = Vcd - Vcb
Rd = -Vdc
[r.subs(soln).n(4) for r in [Ra,Rb,Rc,Rd]]
```




$$\left [ 19.17, \quad 359.6, \quad 177.1, \quad -15.83\right ]$$



#### Check overal equilibrium


```python
# sum forces in vertical dirn.
(Ra+Rb+Rc+Rd - 180 - 45*8).subs(soln)
```




$$0$$




```python
# sum moments about left
(-Rb*6 - Rc*(6+8) -Rd*(6+8+6) + 180*4 + 45*8*(6 + 8/2.)).subs(soln)
```




$$0$$




```python
Ra.expand()
```




$$- \frac{EI \theta_{a}}{6} - \frac{EI \theta_{b}}{6} + 46.6666666666667$$




```python

```

f636d9a51652ad3c0eec3d11bd4983549d8b9e82
ipynb
Jupyter Notebook
slope-deflection/oiq-exam-question-1-Version-2.ipynb
nholtz/structural-analysis
246d6358355bd9768e30075d1f6af282ceb995be
CC0-1.0
2016-05-26T07:01:51.000Z
2019-05-31T23:48:11.000Z
slope-deflection/oiq-exam-question-1-Version-2.ipynb
nholtz/structural-analysis
246d6358355bd9768e30075d1f6af282ceb995be
CC0-1.0
slope-deflection/oiq-exam-question-1-Version-2.ipynb
nholtz/structural-analysis
246d6358355bd9768e30075d1f6af282ceb995be
CC0-1.0
2016-08-30T06:08:03.000Z
2016-08-30T06:08:03.000Z
Qwen/Qwen-72B
1. YES
2. YES