Question $1$

For the non$-$parallel chord truss bridge, $x=5m$ and $y=3m.$

$(1)$ Determine the influence lines for $F_{CD}(F_1),F_{Cd}(F_2)$ :

$(2)$ The bridge is to be designed for the equivalent moving load detailed below with $P=$

$115kN$ and $q=10k\frac{N}{m}.$ Compute the maximum tensile and compressive axial forces in member

Cd $(F_2).$

Hint: Assume tensile forces when establishing relationships between axial forces of

members and reaction forces

For members CD and Cd:

Left Hand Freebody:

b$)$

Determine the relationships between $F_2$ and $R_g,$ and $F_2$ and $R_a$ :

When the unit load moves between a to $c,$ use the right hand freebody and choose the appropriat

equation to be used

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0{\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0{\displaystyle \underset{?}{\overset{?}{}}}M=0$

Only when ${\displaystyle \underset{?}{\overset{?}{}}}M=0$ is selected, please indicate about which point the moment equation should

written

Point D Point d Point E Point $E$

You can obtain $F_2=,R_g($Fill in the actual value together with positive or negative sign$)$

When the unit load moves between $d$ to $g,$ use the left hand freebody and choose the appropriate

equation to be used

$F_x=0,{\displaystyle \underset{y}{\overset{?}{}}}=0,{\displaystyle \underset{?}{\overset{?}{}}}M=0$

Only when ${\displaystyle \underset{?}{\overset{?}{}}}M=0$ is selected, please indicate about which point the moment equation should be

written

Point b Point c Point B Point C

You can obtain $F_2=,R_a($Fill in the actual value together with positive or negative sign$)$

Influence line for $F_{Cd}(F_2)$ :

Fill in the absolute values and indicate the appropriate directions of the movement of the following

points:

Ordinate value of Point $a=$

$"+"($Move upward$)"-"($Move downward$)$ No movement

Ordinate value of Point $c=$

$"+"($Move upward$)"-"($Move downward$)$ No movement

Ordinate value of Point $d=$

$"+"($Move upward$)"-"($Move downward$)$ No movement

Ordinate value of Point $g=$

$"+"($Move upward$)"-"($Move downward$)$

a$)$

Determine the relationships between $F_1$ and $R_g$ and $F_1$ and $R_a$ :

When the unit load moves between a to $c,$ use the right hand freebody and choose the appropriate

equation to be used

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$@$F_y=0$@$M=0$

Only when ${\displaystyle \underset{?}{\overset{?}{}}}M=0$ is selected, please indicate about which point the moment equation should be

written

Point D Point d Point E Point e

You can obtain $F_1=,R_g($Fill in the actual value together with positive or negative sign$)$

When the unit load moves between $d$ to $g,$ use the left hand freebody and choose the appropriate

equation to be used

${\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0F_y=0$@$M=0$

Only when ${\displaystyle \underset{?}{\overset{?}{}}}M=0$ is selected, please indicate about which point the moment equation should be

written

Point c Point d Point C Point D

You can obtain $F_1=,R_a($Fill in the actual value together with positive or negative sign$)$

Influence line for $F_{CD}(F_1)$ :

Fill in the absolute values and indicate the appropriate directions of the movement of the following

points

Ordinate value of Point $a=$

$"+"($Move upward$),"($Move downward$)$

Ordinate value of Point $c=$

$""+"($Move upward$),"*($Move downward$)$

Ordinate value of Point $d=$

$"+"($Move upward$)"-"($Move downward$)$ No movement

Ordinate value of Point $g=$

$"+"($Move upward$)"-"($Move downward$)$ No movement