Question $1$

For the non$-$parallel chord truss bridge, $x=4m$ and $y=2\mathrm{.}5m.$

$(1)$ 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:

Right Hand Freebody: a$)$

Determine the relationships between F$1$ and Rg$,$ and F$1$ and Ra:

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

Answer for part Gap $0$

$$Fx$=0$

$$Fy$=0$

$$M$=0$

Only when $$M$=0$

is selected, please indicate about which point the moment equation should be written

Answer for part Gap $1$

Point D

Point d

Point E

Point e

You can obtain F$1=$

Rg $($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

Answer for part Gap $3$

$$Fx$=0$

$$Fy$=0$

$$M$=0$

Only when $$M$=0$

is selected, please indicate about which point the moment equation should be written

Answer for part Gap $4$

Point c

Point d

Point C

Point D

You can obtain F$1=$

Ra $($Fill in the actual value together with positive or negative sign$)$

Influence line for FCD $($F$1)$:

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

Ordinate value of Point a $=$

Answer for part Direction of Point a

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point c $=$

Answer for part Direction of Point c

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point d $=$

Answer for part Direction of Point d

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point g $=$

Answer for part Direction of Point g

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Unanswered

b$)$

Determine the relationships between F$2$ and Rg$,$ and F$2$ and Ra:

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

Answer for part Gap $0$

$$Fx$=0$

$$Fy$=0$

$$M$=0$

Only when $$M$=0$

is selected, please indicate about which point the moment equation should be written

Answer for part Gap $1$

Point D

Point d

Point E

Point e

You can obtain F$2=$

Rg $($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

Answer for part Gap $3$

$$Fx$=0$

$$Fy$=0$

$$M$=0$

Only when $$M$=0$

is selected, please indicate about which point the moment equation should be written

Answer for part Gap $4$

Point b

Point c

Point B

Point C

You can obtain F$2=$

Ra $($Fill in the actual value together with positive or negative sign$)$

Influence line for FCd $($F$2)$:

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

Ordinate value of Point a $=$

Answer for part Direction of Point a

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point c $=$

Answer for part Direction of Point c

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point d $=$

Answer for part Direction of Point d

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Ordinate value of Point g $=$

Answer for part Direction of Point g

$"+"($Move upward$)$

$"-"($Move downward$)$

No movement

Unanswered

c$)$

Compute the maximum tensile and compressive axial forces in member Cd $($F$2)$:

For F$2,$max$($T$),$ P should be positioned at

Answer for part Gap $1$

Point e

Point f

Point d

Point g

ForF$2,$max$($T$),$ q should be positioned at

Answer for part Gap $2$

Over the whole span of the bridge

Over the positive influence line region

Over the negative influence line region

The maximum tensile axial force in member Cd$,$ F$2,$max$($T$)=$

kN $($Fill in the absolute value$)$

For F$2,$max$($C$),$ P should be positioned at

Answer for part Gap $4$

Point a

Point c

Point b

Point d

ForF$2,$max$($C$),$ q should be positioned at

Answer for part Gap $5$

Over the whole span of the bridge

Over the positive influence line region

Over the negative influence line region

The maximum compressive axial force in member Cd$,$ F$2,$max$($C$)=$

kN $($Fill in the absolute value$)$