Resources for Structural Engineers and Engineering Students

### Question 2

$\theta=\frac{1}{EI} [ 0.333 wLx^2 - 0.167 wx^3- 0.0417 \frac{wx^4}{L} - 0.0611 wL^3 ]$
$\Delta=\frac{1}{EI} [ 0.111 wLx^3 - 0.0417 wx^4- 0.00833 \frac{wx^5}{L} - 0.0611 wxL^3 ]$

### Question 3

$\theta = \begin{cases} \frac{1}{EI}[Mx-\frac{PLx}{2}+\frac{Px^2}{2}] & \quad \text{if } 0 < x < \frac{L}{2}\\ \frac{1}{EI}[Mx-\frac{PL^2}{8}] & \quad \text{if } \frac{L}{2} < x < L\\ \end{cases}$
$\Delta = \begin{cases} \frac{1}{EI}[\frac{Mx^2}{2}-\frac{PLx^2}{4}+\frac{Px^3}{6}] & \quad \text{if } 0 < x < \frac{L}{2}\\ \frac{1}{EI}[\frac{Mx^2}{2}-\frac{PL^2x}{8}+\frac{PL^3}{48}] & \quad \text{if } \frac{L}{2} < x < L\\ \end{cases}$

### Question 4

$\theta_{mid} = {2.2^\circ}\curvearrowright$, $\Delta_{mid} = 75.8\mathrm{\,mm}\downarrow$, $\theta_{B} = {2.5^\circ}\curvearrowright$, $\Delta_{B} = 225\mathrm{\,mm}\downarrow$

### Question 5

$\theta_{B,left} = {0.74^\circ}\curvearrowright$, $\Delta_{B} = 55.9\mathrm{\,mm}\downarrow$, $\theta_{B,right} = {0.69^\circ}\curvearrowleft$, $\Delta_{D} = 30.5\mathrm{\,mm}\downarrow$

### Question 6

Local maximum deflection of $44.4\mathrm{\,mm}\uparrow$ at $x=3.15\mathrm{\,m}$
Absolute maximum deflection of $1410\mathrm{\,mm}\downarrow$ at $x=13\mathrm{\,m}$ (end of cantilever at point C)

### Question 7

Absolute maximum deflection of $154\mathrm{\,mm}\downarrow$ at $x=5.59\mathrm{\,m}$

### Question 8

Same answers as question 5.

### Question 9

$\theta_{D} = {0.25^\circ}\curvearrowleft$, $\Delta_{B} = 0$, $\theta_{B} = {2.0^\circ}\curvearrowright$, $\Delta_{D} = 52.2\mathrm{\,mm}\uparrow$

### Question 10

$\theta_{C} = {0.12^\circ}\curvearrowright$, $\Delta_{C} = 3.59\mathrm{\,mm}\downarrow$, $\theta_{B} = {0.136^\circ}\curvearrowright$, $\Delta_{B} = 10.3\mathrm{\,mm}\downarrow$

### Question 11

$I \geqslant 132\times 10^6\mathrm{\,mm^4}$

### Question 12

$I \geqslant 1717\times 10^6\mathrm{\,mm^4}$

### Question 13

$\Delta_C = 263\mathrm{\,mm}\downarrow$

### Question 14

$\theta_{A} = {0.047^\circ}\curvearrowright$, $\Delta_D = 1.27\mathrm{\,mm}\downarrow$

### Question 15

$I \geqslant 430\times 10^6\mathrm{\,mm^4}$

### Question 16

$I \geqslant 2260\times 10^6\mathrm{\,mm^4}$

### Question 17

$\Delta_C = 0.557\mathrm{\,mm}\uparrow$

### Question 18

$\theta_{A} = {1.70^\circ}\curvearrowleft$, $\Delta_A = 120\mathrm{\,mm}\downarrow$

### Question 19

$\theta_{D} = {0.769^\circ}\curvearrowright$, $\Delta_E = 61.3\mathrm{\,mm}\rightarrow$

### Question 20

$\Delta_B = 1.44\mathrm{\,mm}\downarrow$, $\Delta_H = 9.15\mathrm{\,mm}\rightarrow$

### Question 21

$\Delta_C = 7.83\mathrm{\,mm}\uparrow$, $\Delta_F = 0.780\mathrm{\,mm}\downarrow$

### Question 22

$A \geqslant 227\mathrm{\,mm^2}$

### Question 23

$A \geqslant 550\mathrm{\,mm^2}$

### Question 24

$\Delta_F = 2.40\mathrm{\,mm}\rightarrow$

### Question 25

$\Delta_B = 2.50\mathrm{\,mm}\uparrow$