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 ÷ ℓ2, where I (the cross section&a;s second moment of area) is min(b, h)3max(b, h) ÷ 12 and ℓ 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(yC − yA) + FB, y, BC(xC − xA) = ρb(∫xAxB((hABℓABxB − xA + yA − (yA + yB − yAxB − xA(x − xA)))(x − xA)dx) + ∫xBxC((hBCℓBCxC − xB + yA − (yB + yC − yBxC − xB(x − xB)))(x − xA)dx)) + σcars∫xAxC((x − xA)dx) + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(∫0 ftxB − xA((hABℓABxB − xA + yA − (yA + yB − yAxB − xAx))xdx) + ∫xB − xAxC − xA((hBCℓBCxC − xB + yA − (yB + yC − yBxC − xB(x − xB + xA)))xdx)) + σcars∫0 ftxC − xA(xdx) + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(∫0 ftxB − xA((hABℓABxB − xA − yB − yAxB − xAx)xdx) + ∫xB − xAxC − xA((hBCℓBCxC − xB − (yB − yA) − yC − yBxC − xB(x − (xB − xA)))xdx)) + σcars∫0 ftxC − xA(xdx) + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(∫0 ftxB − xA((hABℓABxB − xA − yB − yAxB − xAx)xdx) + ∫xB − xAxC − xA((hBCℓBCxC − xB − (yB − yA) − yC − yBxC − xBx + (yC − yB)(xB − xA)xC − xB)xdx)) + σcars∫0 ftxC − xA(xdx) + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(∫0 ftxB − xA((hABℓABxB − xA − yB − yAxB − xAx)xdx) + ∫xB − xAxC − xA((hBCℓBC − (yC − yB)(xB − xA)xC − xB − (yB − yA) − yC − yBxC − xBx)xdx)) + σcars∫0 ftxC − xA(xdx) + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb((hABℓAB2(xB − xA)x2 − yB − yA3(xB − xA)x3)0 ftxB − xA + (hBCℓBC − (yC − yB)(xB − xA) − (yB − yA)(xC − xB)2(xC − xB)x2 − yC − yB3(xC − xB)x3)xB − xAxC − xA) + σcars(12x2)0 ftxC − xA + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(hABℓAB(xB − xA)2 − (yB − yA)(xB − xA)23 + hBCℓBC − (yC − yB)(xB − xA) − (yB − yA)(xC − xB)2(xC − xB)((xC − xA)2 − (xB − xA)2) − yC − yB3(xC − xB)((xC − xA)3 − (xB − xA)3)) + σcars2(xC − xA)2 + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
FB, x, BC(yC − yA) + FB, y, BC(xC − xA) = ρb(hABℓAB(xB − xA)2 − (yB − yA)(xB − xA)23 + hBCℓBC − (yC − yB)(xB − xA) − (yB − yA)(xC − xB)2(xC − xB)(xC2 − 2xCxA + xA2 − xB2 + 2xBxA − xA2) − yC − yB3(xC − xB)((xC − xA)3 − (xB − xA)3)) + σcars2(xC − xA)2 + Ftruck(xtruck − xA)(xtruck ∈ (xA, xC))
Rotational equilibrium of BC about B
Horizontal equilibrium of BC
Vertical equilibrium of BC
Site 4
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (128 ft, 0 ft), over pin 2 at (88 ft, −7.5 ft).
Site 5
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (192 ft, 0 ft), over pin 2 at (80 ft, −64 ft).
Island 2
(Central Mainland)
Site 1
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (192 ft, 0 ft), over pin 2 at (64 ft, −32 ft) and pin 3 at (128 ft, −32 ft).
Site 3
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (192 ft, 0 ft), over pin 2 at (56 ft, −64 ft) and pin 3 at (136 ft, −64 ft).
Site 5
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (224 ft, 0 ft), over pin 2 at (128 ft, −16 ft).
Site 6
The road passes from point A at (0 ft, 0 ft) to point B at (160 ft, 0 ft). Arch CED passes through pin C at (0 ft, −16 ft), pin E at (80 ft, yE), and pin D at (160 ft, −16 ft), where yE ∈ (−16 ft, 0 ft).
Circle at pin C
(0 ft − 80 ft)2 + (−16 ft − yCED)2 = rCED2
yCED2 + 32 ft ⋅ yCED + 6656 ft2 = rCED2
Circle at pin E
(80 ft − 80 ft)2 + (yE − yCED)2 = rCED2
yCED2 − 2yEyCED + yE2 = rCED2
yCED2 + 32 ft ⋅ yCED + 6656 ft2 = yCED2 − 2yEyCED + yE2
2yEyCED + 32 ft ⋅ yCED = yE2 − 6656 ft2
yCED = yE2 − 6656 ft22yE + 32 ft
rCED = |yE − yCED|
y = yCED + (rCED2 − (x − 80 ft)2)1/2
Rotational equilibrium of bridge about pin C
160 ft ⋅ FD, y = ∫0 ft160 ft((640 lb/ft − 145 lb/ft3 ⋅ 12 ft ⋅ (yCED + (rCED2 − (x − 80 ft)2)1/2))x ⋅ dx) + xtruck ⋅ 72 klb
160 ft ⋅ FD, y = 640 lb/ft ⋅ ∫0 ft160 ft(x ⋅ dx) − 1.74 klb/ft2 ⋅ (yCED∫0 ft160 ft(x ⋅ dx) + ∫0 ft160 ft((rCED2 − (x − 80 ft)2)1/2x ⋅ dx)) + xtruck ⋅ 72 klb
160 ft ⋅ FD, y = 640 lb/ft ⋅ (x2/2)0 ft160 ft − 1.74 klb/ft2 ⋅ (yCED(x2/2)0 ft160 ft − ((rCED2 − (x − 80 ft)2)1/2(rCED2 − x2 + 40 ft ⋅ x + 3200 ft2)/3 + 40 ft ⋅ rCED2atan(80 ft − x(rCED2 − (x − 80 ft)2)1/2))0 ft160 ft) + xtruck ⋅ 72 klb
160 ft ⋅ FD, y = 8192 klb⋅ft − 1.74 klb/ft2 ⋅ (yCED ⋅ 12800 ft2 − ((rCED2 − (x − 80 ft)2)1/2(rCED2 − x2 + 40 ft ⋅ x + 3200 ft2)/3 + 40 ft ⋅ rCED2atan(80 ft − x(rCED2 − (x − 80 ft)2)1/2))0 ft160 ft) + xtruck ⋅ 72 klb
Island 3
(Ridge)
Site 1
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (256 ft, 0 ft), over pin 2 at (32 ft, −64 ft) and pin 3 at (224 ft, −64 ft).
Site 2
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (192 ft, 0 ft), over pin 2 at (96 ft, −96 ft).
Site 5
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (384 ft, 0 ft), over pin 2 at (0 ft, −48 ft), pin 3 at (192 ft, −16 ft), and pin 4 at (384 ft, −48 ft).
Site 6
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (224 ft, 0 ft), over pin 2 at (8 ft, −64 ft).
Site 8
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (320 ft, 0 ft), over pin 2 at (32 ft, −96 ft) and pin 3 at (288 ft, −96 ft).
Island 4
(Eastern Mainland)
Site 1
The road passes from pin 0 at (0 ft, 0 ft) to pin 1 at (96 ft, 0 ft), over pin 2 at (96 ft, −16 ft).