BOLIVIA BRIDGE MANUALBrianne Connolly

Ben GagneCatherine Joseph

Magdalena Kelleher

TABLE OF CONTENTS

Justification for specific dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Materials List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Flow rate calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Force calculations: Max Bending Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-11

Force calculations: Flow force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Force calculations: Hydrostatic force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Force calculations: Total force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Single culvert forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14-15

Strip Footing Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16-18

Construction sequence and timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Details ……….. . . . …. . . ….. . . . . ….. . …. . . . . ….. . . . . . . …. …. …. . . . . . . . . . . 20

Operation and Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-21

Work Left to Do.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …..22

Design drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23-25

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JUSTIFICATION FOR SPECIFIC DIMENSIONS

After taking surveying data at each cross-section, the bridge will be built at Obrajes 1, cross-section 3.

See attached Obrajes1_v8.

The surveying data points for this site were not taken exactly in a straight line, so raw

data was approximated by the equation along the surface of the

earth, with known varying depths at each point. This yielded a span of 28.15 m, a max depth of 1.204 m, and an average depth of .494 m. The slope of the river was found to be -.04551 radians, using the midpoints of the bridge site cross-section and a cross-section of points taken upstream.

Obrajes 1 Obrajes 2 Iruma Jachuma Condor ChinokaSpan(m) 30.28614 24.81772 50.48708 40.88897211 58.55314099Max Depth(m) 1.20396 1.459992 0.381 1.2192 1.024128Avg. Depth (m) 0.494053 0.429971 0.195411 0.35052 0.396101455

Culvert size:We chose to use the 2-meter diameter culverts and cut them in half so we could have optimal flow and reduce material costs. The culverts will each be 4.556 meters long. This will allow for a 3.048 meter roadway as well as a retaining wall with a 45° angle top, while still allowing 0.5 meter of culver extending beyond the wall.

Width of the Roadway:Our roadway is 3.048 meters (10ft) wide; an appropriate width for the level of traffic of the site. Making the bridge too wide would create unnecessary costs, however a bridge that is too narrow would not meet the purpose of the bridge. We concluded that 10 feet would be a suitable width for the bridge.

Angle of ends of the bridge:The roadway's beginning and end are both sloped at 15° angle since the roadway is built at a level higher than the embankment. This will allow for a smooth transition onto the roadway for cars and pedestrians at not too steep of an incline.

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MATERIALS LIST

Item Amount Total Cost Acquired from:2000mm metal pipe culverts

6 (sliced in half)

4.556 m long

$8615 Oruro

Portland Cement OruroAggregate (concrete) OruroSoil 29.0442 m3

total-- Riverbed excavation

Crushed Stone (Gravel) 8.092 m3 7 truckloads

$220 Oruro

Wood – concrete forms -- -- Local Scrap Wood

Equipment Needed120 L Gas Concrete mixer

1 $1000 Oruro

Level (18”) 2 $5 OruroShovels (flathead) 20-30 $245-$365 OruroWheelbarrows 5 $430bs Oruro

Notes: Total Costs were converted from “bs” to “$.”We overestimated on all costs by rounding up to the nearest five or zero on all estimates. Also, we will have more than enough soil from the riverbed excavation for filling in around the culverts.

Assumptions for culverts:We assumed the price was in dollars and that a 2m diameter pipe would cost 1.5 more that a 1m diameter pipe. We also assumed the cost was per meter. Our cost does not include cost of cutting or delivery.

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FLOW RATE CALCULATIONS

To calculate the volumetric flow rate of the river we used Manning's formula,

where k is equal to 1.0 because we're using SI units, n is the manning coefficient of roughness, Rh is the hydraulic radius, and S is the slope of the riverbed. We used the manning coefficient of 0.035 which is used for floodplains, pastures, and farmlands. The hydraulic radius is equal to A/P, where A is the cross sectional area and P is the wetted perimeter. We calculated the river's cross sectional area with AutoCAD, which yielded an area of 18.9554 m2, as well as the wetted perimeter, which was 56.9150 m. The slope S was determined by using a point in the middle cross section and the midpoint of a cross-section upstream. This equaled 0.0455 m/m.

By plugging in these numbers into Manning's formula, we found the velocity of the river to be 2.9 m/s. We then took this velocity and plugged it into the continuity equation: Q = AV, where Q is flow rate, A is the cross sectional area, and V is the velocity. The final flow rate came out to be 55.5062 m3/s.

Once we determined the max flow rate of the river, we looked into figuring out the flow rate going through the half culverts to make sure we had a sufficient number. To do this, we used Dr. Kabala's colebrook.m file to calculate volumetric flow rate allowed by semi-circular, 2-meter diameter culverts for our riverbed conditions.

This yielded a flow rate of 5.13568 m3/s per culvert. Based on this number, we determined that 10.8 culverts were needed. Therefore our ultimate design has 11 half-culverts.

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FORCE CALCULATIONS: MAX BENDING MOMENT

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The maximum bending moment from the dead load is 1053.6 N-m. The maximum bending moment from combined loads was found to be 1354.5 N-m. We will have to check manufacturer’s specifications to ensure these moments can be withstood, though if the culverts are the kind normally used for highway construction, this should not pose a problem. The loss in strength of the culvert arch will be diminished by placing the bottoms of the arches in concrete.

FORCE CALCULATIONS: FLOW FORCE

10

hp

ph

x

= 2.9 m/s

Q = AV = 55.5062 m3/s

N

Pa

FORCE CALCULATIONS: HYDROSTATIC FORCE

Pa

11

totp

x

0FORCE CALCULATIONS: TOTAL FORCE

Pa

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SINGLE CULVERT FORCES

Calculations of Downward Forces on a Single Culvert:These were calculated using the diameter of the culvert as the boundaries of the width. Thus, the width was 2 meters. The other measurements were determined from the plan view and side view of the design. The density values used were found from the simetric.co.uk website with address http://www.simetric.co.uk/si_materials.htm. The value used for concrete is specific for Portland cement with limestone aggregate. The value used for gravel is for loose, dry gravel. The value used for soil is for dry, compacted soil. These conditions are the most similar to the conditions that will affect our bridge.

Soil:Volume = Total – volume of culvert = [(3.048m)(1.3048m)(2m)-(1/2)(π)(1)2(3.048m)] = 3.16627m3

F = (3.16627m3)(18,000N/m3) = 56,992.86N

Retaining Wall:Volume(1wall) = Total – volume of culvert = [(3.048m)(.254m)(2m)-(1/2)(π)(1)2(.254m)] = 1.149404m3

F = (1.149404m3)(2371kg/m3)(9.81m/s2) = 26,734.57N2 Walls = 53,469.14766 N

Road:Volume = (.1016m)(2.7561m)(2m) = 0.56004m3

F = (0.56004m3)(2371kg/m3)(9.81m/s2) = 13,206.25598N

Gravel:Volume = (.1016m)(2.8561m)(2m) = 0.58036m3

F = (0.58036m3)(1522kg/m3)(9.81m/s2)

Angled Section of Wall:Volume = (0.0672m2)(2m) = .1344m3 (area found using AutoCAD)F = (.1344m3)(2371kg/m3)(9.81m/s2) = 3,126.078144N

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Calculation of Downward Forces of Vertical Column of Materials between Two Culverts:The width used was .2 meters which is the distance between the edges of the culverts and was extended vertically for the entire height of the structure. The density values are the same as were used in the first calculations.

Soil:Volume = (3.048 m)(1.3048 m)(0.2 m) = 0.79540608 m3

F = (.6308140 m3)(18000 N/m3) = 14, 317.30944 N

Retaining Wall:Volume = (3.048 m)(0.254 m)(0.2 m) = 0.1548384 m3

F = (0.1548384 m3)(2371 kg/m3)(9.81 m/s2) = 3,601.465313 N2 Wall = 7,202.930626 N

Road:Volume = (0.1016 m)(2.8561 m)(0.2 m) = 0.05803392 m3

F = (0.05803392 m3)(2371 kg/m3)(9.81 m/s2) = 1,302.624482 N

Gravel:Volume = (.1016 m)(2.8561 m)(0.2 m) = 0.05803392 m3

F = (0.05803392 m3)(1522 kg/m3)(9.81 m/s2) = 866.5243528 N

Angled Section of Wall:Volume = (0.0672 m2)(0.2 m) = 0.01344 m3

F = (0.01344 m3)(2371 kg/m3)(9.81 m/s2) = 312.6078144 N

Strip Footing calculations:Weights acting down on the strip footing wall (Please refer to SINGLE CULVERT FORCES for calculations):

Soil = 14,317.30944 NCrushed stone (gravel) = 866.5243528 NRetaining wall = 7202.930626 NConcrete roadway = 1302.624482 NAngled section of wall = 312.6078144 NTruck = 17,792.8864 – 31,137.5512 N

fc’ (compressive strength) = 3500 psify (yielding strength) = 40 ksi (?)Pallow = 1000 – 1500 psf

Conversions: Soil = 14,317.30944/3.048 (N/m) =

= 0.321866 k/ft

Crushed stone = 866.5243528/3.048 (N/m) = 0.01948 k/ftConcrete wall = 7202.930626/((2)(0.254)) (N/m) = 0.97157 k/ftConcrete roadway = 1302.624482/3.556 (N/m) = 0.025101 k/ftAngled section of wall = 312.6078144/ 0.4003 (N/m) = 0.053511 k/ft

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Truck = 17792.8864/3.556 (N/m) = 0.342857 k/ft or 31137.5512/3.556 (N/m) = 0.6 k/ft

PD = add up bridge conversions = 0.321866 + 0.01948 + 0.97157 + 0.025101 + 0.053511 = 1.39153 k/ftPL = truck conversion = 0.6 k/ft (use because it is the heaviest the truck load could be)

1) take unit length of wall of footing2) determine width so as not to exceed allowable soil bearing pressure3) determine thickness of footing such that shear reinforcement is NOT required4) design flexural reinforcement5) check development lengths6) add temperature & shrinkage reinforcement (perpendicular to flexural

reinforcement)7) sketch final design

1) Take unit length2) service load P = PD + PL = 1.39153 + 0.6 = 1.99153 k/ft

area required = P/Pallow = 1.99153/1.0 = 1.99153 ft2

Since we assumed unit length, B = width = 1.99153 ft Round the width to 2 ft

3) Assume a thickness of 1/6 the width, d = (1/6)(2) = 0.333 ft = 0.5 ft = 6 inLength of critical section = [((2)(12) – 0.5(10 in))/2] – 6 = 3.5 infactored load = 1.2(PD) + 1.6(PL) = 1.2(1.39153) + 1.6(0.6) = 2.62984 k/ft(2.62984 k/ft)(1 ft) = 2.62984 kips over 1 unit length sectionfactored bearing pressure = 2.62984 kips/2 ft = 1.31492 k/ftVu = (1.31492 k/ft)(3.5/12) = 0.383518 kipsVn = Vc + Vs = Vc since Vs = 0 (there are no stirrups)Vn = 2 (bw)(d) = 2 (12 in)(6 in) = 8519.15 lbs = 8.51915 kips( )(Vn) = (0.75)(8.51915 kips) = 6.38937 kips6.38937 kips > 0.383518 kips

4) [((2)(12) – 0.5(10))/2] = 9.5 inVmax = (1.31492 k/ft)(9.5 in)(1/12) = 1.04098 kipsMmax = (1/2)(9.5 in)(-1.04098 kips) = -4.94465 k-in = -0.412054 k-ftMn = Mu/ = 0.412054/0.9 = 0.457838 k-ft

12.7177 psi

and m = fy/[(0.85)(fc')] = 40/[(0.85)(3.5)] = 13.4454

0.000319

Calculate area of steel: As = bd = (0.000319)(12 in)(6 in) = 0.022941 in2

Pick steel using Table A-9 (Areas of Bars in a Section 1 ft Wide):#3 bars at 18" on center (As = 0.07 in2)

5) Using simplified method, category B (# 6 bars or smaller):

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where =1.0 (non-top bar) = 1.0 (uncoated) = 1.0 (normal weight aggregate concrete) db = 0.375 in

15.2128 in = 1.26773 ft

[((2)(12) – 0.5(10))/2] = 9.5 in > 15.2128 in NO** because there is not enough development length, increase B from 2 ft to 4 ft.[((4)(12) – 0.5(10))/2] = 21.5 in, which is now greater than 15.2128 in needed for developmentB = 4 ft

6) As,min = 0.0020(b)(h) for Grade 40 rebarAs,min = 0.0020(4(12))(6) = 0.576 in2

Maximum spacing = 5x thickness or 18" (minimum of the two)d = 6 in add 3" of clear cover + (0.375/2) and the thickness = 9.1875 in5(9.1875) = 45.9375 in > 18 inSo the maximum spacing is 18 inUse 5-#3 bars at 18" on center (temperature and shrinkage steel)Use #3 bars at 18" on center (flexural reinforcement)

7) Final Design:

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CONSTRUCTION SEQUENCE AND TIMELINE

Task Day1. Obtain materials on list 12. Have pipes cut and delivered 13. Dig out riverbed to achieve flat bed 14. Sequence for placing culverts 15

a. Set forms for strip footing b. Pour concrete (partial) and place rebar c. Place culverts in forms d. Pour concrete in forms (securing culverts) e. Cut and place concrete retaining wall forms(inlet & outlet) f. Pour concrete in wall forms g. Place soil fill between retaining walls (compacted)5. Place angled concrete wall/curb 236. Place crushed stone to prep for roadway 267. Lay concrete roadway 28

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DETAILS

Detailed description of Construction Timeline Step 3:In order to fit 11 half culverts into the riverbed and achieve maximum flow in each, the riverbed will need to be dug out on both ends (Please refer to Profile View in Design drawings). By digging out the riverbed to a level equal to the lowest point of the cross section, we can ensure that the water will be able to flow through the culverts adequately.

Detailed description of Construction Timeline Step 4:Our sequence for placing the culverts will be a sequential and simultaneous process. The first stage of the process will be to set the form for the first two strip footings, pour the concrete, place rebar, and place the first culvert in the forms. The concrete will be poured into the first footing, securing the culvert in place. The form for the first section of the concrete wall will be cut and placed, and the concrete for the wall will be poured. Once the wall has had time to set, a second crew will begin filling around the culvert with compacted soil while the first crew begins on the third strip footing and placing the second culvert. Once the second footing has been poured and the concrete wall has been poured and had time to set, the soil crew will follow behind. This process will continue as the bridge is built across the river. By the time both crews reach the other side, the strip footings, culverts, concrete wall, and compacted soil fill will all be in place. The construction process will then continue with the placing of the angled concrete wall/curb. (Please refer to CONSTRUCTION SEQUENCE AND TIMELINE)

OPERATION AND MAINTENANCE

Safety factors:We have added safety factors in various aspects of our design. We must also consider other failure modes for culverts and prepare for these failures in the chance that they occur. The most common failure modes for culverts are insufficient capacity, plugging, and embankment erosion.

Preventative MeasuresInsufficient capacity:

- Install armoring and wing-walls at the entrance and outlet of the culvert to increase pressure of the flow through culverts.

- Install a relief culvert.

Plugging:- Install an entrance debris deflector.- Install a sediment catch basin upstream.- Install a relief culvert.

Embankment Erosion:- Place riprap to reduce embankment erosion.- Shape culvert entrance to match embankment slope.- Construct flared end section to direct flow.

How Often:Maintenance of the bridge will require periodic bridge inspections. At the time of completions, an initial inspection will occur. The purpose of this inspection is to reevaluate site conditions and identify deficiencies that may not have been identified during construction. This includes reevaluation of erosion, debris guards, and grades of banks.

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Routine inspections will be regularly scheduled, occurring every two years during the dry season. Inspection of equipment of bridge evaluation tools will occur first (cleaning tools, visual aid tools, measuring equipment, safety equipment, etc.). The bridge inspector will inspect the bridge for fractures, structural deficiencies, failures in the metal culverts, and will identify changing conditions.

Interim inspections will occur every six months to identify any quickly changing conditions with the bridge. These inspections may be performed by local (or district) trained inspectors. During these inspections, the inspector should also remove any debris from the debris guards to allow for maximum flow through the culverts.Damage inspections will be performed as needed, generally as a result of environmental damages, fires, collisions, or severe floods. Underwater inspections may be performed as needed during low water seasons. Wading techniques may be used for this inspection. In-depth inspections may also be performed to investigate deficiencies found during routine inspections.

It will also be useful to develop in information database containing all data gathered during bridge inspections. This will help in monitoring load-bearing capacities of the bridge.

Operation Costs:Cost to operate the bridge will be composed of pay for a bridge inspector and funds for future bridge repairs. This will be proportional to the average pay rate for bridge inspectors in Bolivia and the cost of materials for the future repairs necessary. There will be no daily operation cost for the bridge.

Design Work Left to Do:

Design the concrete roadway. The modifications will slightly affect the forces on the culverts, and the max bending moment of the culvert.Design the retaining wall. This will also have a marginal impact on the forces on the culverts.

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