]> Bridge Constructor in Concrete

# Bridge Constructor in Concrete

The site is converted from Bridge Constructor under the assumption that 2.5 meters (the width of a square on the default grid) is equivalent to 8 feet. (In reality, 2.5 m ≈ 8.202 ft.)

The bridge is composed entirely of plain (unreinforced) class A concrete, with density (ρ) 145 lb/ft3, compressive strength (fc′) 4 klb/in2, tensile strength 0 klb/ft2, shear strength 2(fc′ ⋅ 1 lb/in2)1/2, and modulus of elasticity (E) 1820(fc′ ⋅ 1 klb/in2)1/2. The cross section of the bridge has width (b) 12 ft.

If a member of the bridge is directly beneath the riding surface of the bridge, then the member is a filled member. A filled member is separated into a fill part and a load&h;bearing part. The fill part&a;s upper profile and lower profile are defined by two separate functions. The load&h;bearing part&a;s upper profile is identical to the fill part&a;s lower profile, but the load&h;bearing part is designed as if its centerline profile were identical to the fill part&a;s lower profile. The load&h;bearing part has a rectangular cross section with height h. It is assumed that axial load and flexural load are resisted by only the load&h;bearing part, while shear load is resisted by both parts.

If a member of the bridge is not a filled member, then it is an unfilled member. An unfilled member has a rectangular cross section with height h, and its centerline profile is defined by a function. It has buckling strength of π2EI ÷ 2, where I (the cross section&a;s second moment of area) is min(b, h)3max(b, h) ÷ 12 and is the length of the member.

The live load on the riding surface of the bridge consists of: cars, represented with a uniform load of 640 lb/ft; and a truck, represented with a point load of 72 klb.

## Camatuga

### Island 1

(Westlands)

#### Site 3

The road passes: from a point at (0 ft, 0 ft); over points at (48 ft, −24 ft) and (112 ft, −24 ft); to a point at (160 ft, 0 ft).

ABC, CDE, and EFG are three&h;hinge arches.

Rotational equilibrium of ABC about A

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(∫xAxB((hABABxBxA + yA − (yA + yByAxBxA(xxA)))(xxA)dx) + ∫xBxC((hBCBCxCxB + yA − (yB + yCyBxCxB(xxB)))(xxA)dx)) + σcarsxAxC((xxA)dx) + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(∫0 ftxBxA((hABABxBxA + yA − (yA + yByAxBxAx))xdx) + ∫xBxAxCxA((hBCBCxCxB + yA − (yB + yCyBxCxB(xxB + xA)))xdx)) + σcars0 ftxCxA(xdx) + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(∫0 ftxBxA((hABABxBxAyByAxBxAx)xdx) + ∫xBxAxCxA((hBCBCxCxB − (yByA) − yCyBxCxB(x − (xBxA)))xdx)) + σcars0 ftxCxA(xdx) + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(∫0 ftxBxA((hABABxBxAyByAxBxAx)xdx) + ∫xBxAxCxA((hBCBCxCxB − (yByA) − yCyBxCxBx + (yCyB)(xBxA)xCxB)xdx)) + σcars0 ftxCxA(xdx) + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(∫0 ftxBxA((hABABxBxAyByAxBxAx)xdx) + ∫xBxAxCxA((hBCBC − (yCyB)(xBxA)xCxB − (yByA) − yCyBxCxBx)xdx)) + σcars0 ftxCxA(xdx) + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb((hABAB2(xBxA)x2yByA3(xBxA)x3)0 ftxBxA + (hBCBC − (yCyB)(xBxA) − (yByA)(xCxB)2(xCxB)x2yCyB3(xCxB)x3)xBxAxCxA) + σcars(12x2)0 ftxCxA + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(hABAB(xBxA)2(yByA)(xBxA)23 + hBCBC − (yCyB)(xBxA) − (yByA)(xCxB)2(xCxB)((xCxA)2 − (xBxA)2) − yCyB3(xCxB)((xCxA)3 − (xBxA)3)) + σcars2(xCxA)2 + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

FB, x, BC(yCyA) + FB, y, BC(xCxA) = ρb(hABAB(xBxA)2(yByA)(xBxA)23 + hBCBC − (yCyB)(xBxA) − (yByA)(xCxB)2(xCxB)(xC2 − 2xCxA + xA2xB2 + 2xBxAxA2) − yCyB3(xCxB)((xCxA)3 − (xBxA)3)) + σcars2(xCxA)2 + Ftruck(xtruckxA)(xtruck ∈ (xA, xC))

Rotational equilibrium of BC about B

Horizontal equilibrium of BC

Vertical equilibrium of BC