A bascule bridge is designed to be raised to allow passage of ships through the water channel spanned by $($a$)$ LEAF OPEN

$($b$)$ LeAf CLOSED Figure $2$a $-$ AASHTO H$20$ Truck

the bridge. Bascule comes from the French word for $$see$-$saw$$ and is an appropriate description for this

type of bridge as it uses a counterweight to balance the weight of the leaf which crosses the channel. A

diagram of a Single Leaf Simple Trunnion bascule bridge is shown in Figure $2$b$.$

a$)$ Assume that the leaf is in the closed position. The mass of the leaf is $10,000$ kg and the center of

gravity is $8$ m to the left of the trunnion bearing $($the pivot point$).$ The live load bearing support at the left

end of the leaf is $20$ m from the trunnion bearing, the rear break in the deck is $2$ m from the trunnion

bearing and the center of gravity of the counterweight $($CWT$)$ is $4$ m from the trunnion bearing. What is

the mass of the counterweight that should be specified to balance the leaf and make the bridge as easy to

open as possible?

b$)$ An AASHTO H$20$ Truck as shown in Figure $2$a drives across the bridge from left to right.

i$.$ What is the maximum reaction force at the live load bearing and what is the location of

the truck for this loading?

ii$.$ What is the maximum uplift force on the lock bar and what is the location of the truck for

this loading?

iii. What would the solutions for parts i$)$ and ii$)$ be if the truck were travelling in the opposite

direction?

c$)$ In its open position, the leaf makes an angle of $45\backslash$deg with the horizontal. A $4$kN$/$m wind load acts

horizontally from right to left. Assuming a distance of $4$ m from the rack and pinion to the trunnion, what

force must the rack and pinion system be designed to withstand to maintain equilibrium?