Footbridge Maillart's over the Triftwasser River
A Case Study in Reinforced Concrete
GSD 6202 Spring 2000 Kyle Dugdale Jacquie Scott Youngsun Sonn Paul Wolff Tyrone Yang
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Footbridge over the Triftwasser 1932
photos after Max Bill
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Bridge Dimensions
68.88 ft
Length: 68.88 ft Slope 5.72 degrees *Slope of bridge has no impact on reactions and calculations for shearing, bending and torsion.
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Dimensions of Bridge
5.77 4.92
Width of web 1.05 ft Depth of flange 0.39 ft Depth of beam 4.1 ft Cross section width 5.77 ft Pedestrian traffic 4.92 ft
4.1
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Weight of Bridge
VOLUME = (cross-sectional area) x (length) = 438 ft3 DEAD LOAD = volume x (weight of reinforced concrete) = 438 ft3 x 150 lb ft3 = 65768 lb Weight
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Weight of Bridge
VOLUME = (cross-sectional area) x (length) = 438 ft3 DEAD LOAD = volume x (weight of reinforced concrete) = 438 ft3 x 150 lb ft3 = 65768 lb Weight
Weight of side volumes: 89393 lb (Total weight would be 155,161 lbs.)
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Weight of Bridge
VOLUME = (cross-sectional area) x (length) = 438 ft3 DEAD LOAD = volume x (weight of reinforced concrete) = 438 ft3 x 150 lb ft3 = 65768 lb Weight LIVE LOAD (pedestrians) = 27126 lb TOTAL WEIGHT = (dead load) + (live load) = 92894 lb
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Shear and Bending Moment Calculations
Max Moment = 801,500 lb-ft
Max Shear = 46447 lb
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Torsion Calculations
Torsion Moment = (1/2 x Live Load) x Lever Arm = (1/2 x 27126 lb) x 1.44 ft = 19579 lb-ft Torsion at each abutment = 33356 / 2 = 16678 ft-lb
Torsion (perp. to beam)
Bending (along length of beam)
1.44 ft.
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wind calculations
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Reinforcing Patterns
Beam: Skin reinforcement Bending moments Shear
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Reinforcing Patterns
Beam: Skin reinforcement Bending moments Shear
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Reinforcing Patterns
Abutments: Shear Bending moments
Diagonal reinforcing prevents shear
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Bending moments
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Reinforcing Patterns
Slab: Torsion
Horizontal reinforcing on top of beam to counter negative moment due to cantilever.
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calculation necessary of steel reinforcements
4 values: balanced steel maximum steel required steel minimum steel (purely for purposes of calculation) (as calculated by Excel spreadsheet)
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required steel (Excel spreadsheet)
i.e. inches, pounds d
fc fy Es using 1.7x[live load] & 1.4x[dead load] e.g. bending 0.9, shear/torsion 0.85
required steel reinforcement
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balanced steel & maximum steel
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minimum steel
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summary
balanced steel: maximum steel: minimum steel: required steel: 16.15 in2 12.11 in2 2.33 in2 7.017 in2
so, use 10 x No.8 reinforcing bars i.e. 10 x 0.79 in2
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transverse reinforcement
i.e. inches, pounds depth of flange at cross-section for a 1-foot section of the bridge
fc fy Es using 1.7x[live load] & 1.4x[dead load] e.g. bending 0.9, shear/torsion 0.85
required steel, for every foot
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Railing:T-section
200 lb
Section view of rail
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F=200 lb
R=200 lb
Section view of rail
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F=200 lb
d
M= Fd R=200 lb
Section view of rail
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Top
200 lb
d
Bottom
Deflection Shear Bending Moment
Maximum Shear Force : 200 lb Maximum Bending M : 754 lb-ft Maximum Deflection : 0.111 in Distance d : 45.276 in
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