hoskerelab/PE_Civil_Bench huggingface dataset:
Subdiscipline: structural

A suspension bridge of 12 m has 2 three hinged stiffening girders supported by two cables having a central dip of 12 m. The roadwy has a width of 6m. the deadload on the bridge is 5 kN/m^2 while the live load is 10 kN/m^2 which acts on the left half of the span. Determine the shear force and bending moment in the girder at 30m from the left end.

Answer: 0 kN and 6750 KNm
Subdiscipline: structural

A simply supported beam of 6m span is subjected to a concentrated load of 18 Kn at 4m from the left support. calculate the slope at mid span

Answer: -5/EI
Subdiscipline: structural

To a fixed beam of length L, an external moment M is applied at a distance a from the left hand support. Determine the fixed end moments developed, where a+b=L

Answer: Mb(2a-b)/L^2 and Ma(a-2b)/L^2
Subdiscipline: structural

A steel tube is bore of 150 mm, wall thickness 2.25 mm is plugged at each end to form a closed cylilnder with external length of 450 mm. If the tube is filled with oil and is subjected to compressive load if 90kn, determine pressure produced by oil

Answer: 0.267 MN/m^2
Subdiscipline: structural

Hollow cylinder cast iron column is 4m long with both ends fixed. Determine the minimum diameter of the column if it has to carry a safe load of 250 KN with a factor of safety of 5.  Take the internal diameter as 0.8 times the external diameter. Take a=1/1600 in rankine formula and sigma_c = 550 MN/m^2

Answer: 108.8 mm
Subdiscipline: geotechnical

Evaluate the suitability of a 4 ft square footing supporting a 1 ft square column (PD = 75 kips and PL = 25 kips) for an allowable soil pressure of 7 k/ft2 using: a) gross soil pressure; b) net soil pressure; and c) factored net soil pressure. The bottom of the one-foot thick footing is set at 5 ft below grade. The unit weight of soil is given as 125 pcf.

Answer: 6.9 k/ft^2, 6.35k/ft^2, 8.17 k/ft^2
Subdiscipline: geotechnical

A two mile long embankment was constructed for a new highway. The embankment is 12 feet high and 20 feet in width. Due to right-of-way restrictions, retaining walls are used to maintain the width of the embankment at 20 feet for its full height. The total unit weight of the embankment fill is 125 pcf. The embankment is constructed on a sand layer that is more than 100 feet thick. The water table is at a depth of 5 feet below the original ground surface. The total unit weight of the sand is 120 pcf above the ground water table and 130 pcf below the water table. The stress increase at a depth of 15 feet under the center of the embankment is approximately:

Answer: 900 psf
Subdiscipline: geotechnical

Soil from a borrow pit will be used to construct a 250,000 cubic yard highway embankment. Project specifications require that the fill in the embankment be compacted to at least 95% of the Modified Proctor maximum dry density. The material in the borrow pit has the following characteristics: Total Unit Weight: 120.0 pcf Moisture Content: 8.0% Specific Gravity of Soil: 2.66 The Modified Proctor maximum dry density and optimum moisture content are 128 pcf and 13.0%, respectively.  How many gallons of water must be added per cubic yard of borrow to achieve the Modified Proctor optimum moisture content? Assume no loss of water by evaporation during transport from the borrow pit.

Answer: 18 gal/yd^3
Subdiscipline: water resources

A 6-inch diameter well provides drinking water to a town. The well draws water from a 200 feet thick aquifer at the rate of 100 gpm. The resulting cone of depression is a 2000-foot radius from the well. The vadose zone is 50 feet thick and the drawdown at the well is 40 feet.  Due to growth of the town, the need for water will increase to 200 gpm. Determine the resulting drawdown.

Answer: 94 ft
Subdiscipline: water resources

A municipal wastewater with a BOD5 (20 C) of 250 mg/l and suspended solids at 300 mg/l is treated with a primary clarifier which removes 35% BOD5(20C) and 60% suspended solids. The average flow rate is 4 MGD with a peak flow rate of 8 MGD. Assume an effluent BOD5(20C) of 30 mg/l. The wastewater from the primary clarifiers is to be treated using two identical parallel trickling filters. Use the National Research Council equation to determine the required diameters for the two low rate trickling filters. Assume a depth of 6 feet for the trickling filters.

Answer: 187 ft
Subdiscipline: water resources

A 30 MGD wastewater treatment plant provides primary and secondary treatment to domestic wastewater for a town of 300,000. The raw wastewater suspended solids are 200 mg/l and the BOD5 (20C) is 250 mg/l. The primary clarifier removes 60% of the suspended solids and 50 mg/l of BOD5 and the secondary clarifier removes 50% of the suspended solids. The effluent from the wastewater treatment plant contains 20 mg/l suspended solids and 20 mg/l BOD5. The sludge pumped daily to the digesters contains 4% solids, 65% of which are volatile. Digestion at 90° F reduces the volatile solids by 60% producing methane gas having a heat value of 600 BTU per cubic foot of digested sludge at a rate of 15 cubic feet per pound of volatile material destroyed. All the methane gas generated by digestion is used as fuel to heat the digesters and exchanges heat from the engine jacket at 75% efficiency. The effluent from the treatment plant contains 20 mg/l suspended solids and 20 mg/l BOD5(20). Determine the total amount of solids produced each day by the treatment plant. Assume ayield coefficient of 95 lb suspended solids per lbm of BOD5 utilized.

Answer: 51,000 lb/day
Subdiscipline: transportation

No file chosenNo file chosen Consider a four-legged intersection with a single lane for each approach. The intersection is currently signalized with simple two-phase actuated control and a 50- second phase duration for the northbound/southbound approaches with 4-second and 1.5-second change and clearance intervals, respectively. The southbound approach has a saturation flow rate of 1615 vehicles per hour and a queue of 14 vehicles. Assuming a green extension time of 4.5 seconds, the arrival flow rate during the effective green time for the southbound approach is most nearly:

Answer: 290 vehicles per hour
Subdiscipline: structural

Portland cement concrete is required for a pavement that will be exposed to moisture in a severe freeze-thaw environment, with the minimum specified compressive strength at 28 days. Air entrainment is required with the recommended average total air content for severe exposure. Slump should be between 1 in and 3 in (using 3 in for determining the water content). A nominal maximum size aggregate of ¾ in is required. The ingredients chosen include a Type I portland cement with a relative density of 3.20, sand with a fineness modulus of 2.60, and crushed stone with a specific gravity of 2.70 and unit weight of 100 lb/ft^3 . The calculated absolute volume of fine aggregate using the absolute volume method is most nearly:

Answer: 5.79 ft^3
Subdiscipline: transportation

A roadway with a design speed of 110 ft/s is to have a spiral curve transition for a circular curve with a radius of 1,800 ft. The minimum and maximum length of spiral, in feet, respectively, using driver comfort as the design criteria and a maximum lateral offset between the tangent and circular curve of 3.0 ft are most nearly

Answer: 185 ft and 360 ft
Subdiscipline: transportation

The number of equivalent single axle loads for a roadway is approximately 2,500,000. The surface layer consists of 3 inches of asphalt concrete with a structural layer coefficient of 0.44. The second layer consists of a coarse bituminous treated base with a resilient modulus of 195,000 psi. Assume the depth of the base layer is the minimum value based on the reported number of ESAL. The drainage coefficient for the pavement layers is 1.00. The thickness of the subbase, consisting of sandy gravel with a resilient modulus of 15,100 psi and a structural number of 5.72, is most nearly:

Answer: 9.5 inches
Subdiscipline: water resources

50°F water flows through 2,200 ft of 8 in (8.18 in inside diameter) cast iron pipe. The pressure in the pipe drops from 100 psi to 98 psi from end to end. What is the velocity in the pipe, in ft/sec?  for cast iron C=100

Answer: 1.5ft/s
Subdiscipline: water resources

The road section pictured below is designed to carry a 10-year storm event such that no more than one-half of the travel lane is inundated. The road is crowned at a 2% grade from the centerline to the curb. Assume n=0.011. from center line there is 12' of travel lane and 2' of gutter. Based on the design criteria, what is the maximum flow in ft^3 /s that the section can convey on a 4% longitudinal grade?

Answer: 3.8 cfs
Subdiscipline: water resources

A curbed roadway section is shown below. The shoulder slope is 4.0% while the slope of the travel lane is 2.0%. The longitudinal (profile) grade is 3.5% and the Manning’s n for the shoulder area adjacent to the curb is 0.011. What is the minimum width that the shoulder needs to be, in feet, to contain the design flow of 3.0 cfs entirely within the shoulder?

Answer: 4.85 ft
Subdiscipline: surveying

A tangent line connecting Sta. 462+86.25 and Sta. 498+89.26 of a highway location survey has a magnetic bearing of S 87° 15' E. At Sta. 478+89.26 it crosses an existing highway whose bearing is S 62°15' W. The acute angle between the two alignments is most nearly:

Answer:  30°30'
Subdiscipline: geotechnical

A sand cone test was performed on a layer of compacted fill. Ottawa sand (γ = 100 pcf) is used to fill the jar in the testing apparatus. The following data was recorded during the test: Soil sample (from hole) moist weight: 4.62 lb, Soil sample (from hole) oven-dried weight: 4.02 lb, Volume of cone: 0.02 ft3, Weight of jar + sand before test: 12.50 lb, Weight of jar + sand after test: 7.00 lb. A Standard Proctor test was performed on the fill to determine a maximum dry unit weight of 118 pcf. The relative compaction (percent) of the fill is most nearly:

Answer: 97%
Subdiscipline: geotechnical

A continuous footing is 2 ft wide and bears 3 ft below the ground surface in a clean sand with γ = 125 pcf and φ = 34° . Use Terzaghi’s method and assume FS = 2.5. The maximum net allowable bearing capacity (psf) is most nearly:

Answer: 7148 psf
Subdiscipline: geotechnical

A 4-ft square foundation bears on sand at a depth of 3 ft. Groundwater is at a depth of 5 feet. The sand has a moist unit weight,gamma = 112 pcf, saturated unit weight, gamma_sat = 115 pcf, and friction angle, phi = 33 degrees. Determine the maximum allowable net load in kips for this foundation. Use a factor of safety of 3.

Answer: 79.3 kips
Subdiscipline: geotechnical

A town of 10,000 is planning to adopt a method of disposing of the solid waste (refuse) generated by the town. If the town chooses to use a landfill as the chosen method, a square 50 acre site is available at the edge of town. The per capita solid waste generation rate is 1200 lbm per capita year. It is estimated that the final in-place density of the well-compacted refuse will be 1000 lbm per yd^3 . The refuse would be applied and compacted in 24 inch lifts. The landfill height would be limited to 25 feet. The side walls would have a 2:1 horizontal to vertical slope. If the town decides to adopt the landfill method to dispose of refuse, what volume in acrefeet would be available on the 50-acre site with a required 100 feet buffer at the edge of the site and an allowable height of 25 feet.

Answer: 863 acre-ft
Subdiscipline: structural

A 24-ft, concrete beam is simply supported at the ends. It is 12 inches wide and 20 inches deep. It has an exterior exposure, and carries a uniformly distributed live load of 160 pounds per foot, and a uniformly distributed dead load of 400 pounds per foot. At the center there is also a point live load of 7 K and a point dead load of 3.6 K. Use, f’c = 4,000 psi and fy = 60,000 psi. What is the smallest area of reinforcing required for the bending moment?

Answer: 2.45 in^2
Subdiscipline: structural

 A ring with a circular cross section of 600 mm in diameter and a mean radius of 90 mm s subjected to a compressive load of 15 kN. calculate the deflection of the ring along the load line. Take E=200GN/m^2

Answer: 0.0143 mm
Subdiscipline: structural

A chain link is made of a steel rod of 18 mm diameter with straight portion 90 mm in length and ends 90mm in radius. if link is subjected to a load of 15kn calculate deflection of link along the load line. take E=200GN/m^2

Answer: 2.14 mm
Subdiscipline: geotechnical

A continuous footing is constructed at a depth of 5 feet in a uniform sand deposit. The width of the footing is 10 feet. The sand has total unit weight of 130 pcf and a friction angle (φ) of 37°. The depth to groundwater is greater than 100 feet. Assume concentric vertical loading. Use Vesic’s bearing capacity factors for all calculations. What is the approximate ultimate bearing capacity if the bottom of the footing is 10 feet deep?

Answer: 98.8 ksf
Subdiscipline: geotechnical

A continuous footing is constructed at a depth of 5 feet in a uniform sand deposit. The width of the footing is 10 feet. The sand has total unit weight of 130 pcf and a friction angle (φ) of 37°. The depth to groundwater is greater than 100 feet. Assume concentric vertical loading. Use Vesic’s bearing capacity factors for all calculations. Requirements 5A) What is the approximate ultimate bearing capacity of the footing?

Answer: 70850 psf
Subdiscipline: water resources

A bridge is proposed to span a river. The bridge piers will be supported on 12” diameter, steel, closed-end pipe piles (concrete-filled) driven into the medium-dense sand river bottom. The water in the river is 15 feet deep. Laboratory tests indicate that the sand has the following properties: specific gravity Gs = 2.67; void ratio, e = 0.60 The results of a pile load test on a 12” steel pipe pile driven 15 feet into the sand indicated that the unit skin friction on the test pile at a depth of 10 feet into the sand was 350 psf at failure. Also, the ultimate end bearing capacity of the test pile was estimated to be 32.0 kips. Neglect the structural capacity of the pile and settlement in answering the following questions. The ultimate skin friction capacity of a pile embedded 25 ft into the sand river bottom is approximately:

Answer: 29 kips
Subdiscipline: water resources

A wastewater treatment plant has an average flow of 4 MGD, a peak flow of up to 12 MGD, and a MLSS concentration of 2,500 mg/L leaving the aeration basin. The hydraulic retention time in a secondary clarifier is 4 hours under average flow conditions, and there are 2 secondary clarifiers. Given an average flow hydraulic loading rate of 850 gpd/ft2 and an average solids loading rate of 12 lb/day*ft2, what is the approximate depth of the clarifier (ft)?

Answer: 13 ft
Subdiscipline: water resources

A plug flow aeration basin is used for a 12 MGD wastewater treatment plant. Calculate the solids retention time (theta_c) [days] assuming the following characteristics of the plant: Influent organic loading (So) = 250 mg/L Effluent organic loading (Se) = 50 mg/L Hydraulic Retention Time (0) = 6 hours Substrate utilization rate (k) = 0.6 day^-1 Growth Yield, Y = 0.56 lb biomass/lb BOD5 Half Velocity Constant (Ks) = 115 mg/L Endogenous decay rate (ka) = .07 day ^-1 Recycle ratio (Qr/Q) = 0.4

Answer: 11 days
Subdiscipline: water resources

A city of 25,000 treats its domestic wastewater at an activated sludge treatment plant (ASTP) and discharges treated effluent into a receiving stream. The water coming into the ASTP has a BOD5 of 300. The effluent from the treatment plant is discharged at a velocity of 1.0 feet per second through a 24-inch diameter pipe that flows full. The dissolved oxygen of the effluent is 3.0 mg/l. The receiving stream has a flow of 15 cubic feet per second, a summer temperature above the ASTP outfall of 15 degrees C and a dissolved oxygen concentration of 9.0 mg/l. The BOD5 of the stream above the ASTP is 2 mg/l and the ASTP effluent BOD5(20C) is 30 mg/l. If the stream velocity is 0.25 feet per second, and the reaeration coefficient, kr, 20, is 0.25 per day, determine the dissolved oxygen in the stream 25 miles below the outfall. Assume a oxygen saturation level of 10 mg/l for water that is 15.9° C.

Answer: 8.41 mg/l
Subdiscipline: transportation

A four-lane (two lanes in each direction) freeway passes through rolling terrain in an urban area. The freeway is constructed with 11 ft lanes and abutment walls 2 ft from the outer pavement edges of both slow lanes. The one-direction peak hourly volume during the weekday commute is 1800 vph. Traffic includes 3% buses and 5% trucks. The ramp density is one ramp per mile. The peak-hour factor is 0.90. The posted speed limit is 65 mph. (a) What is the passenger car equivalent flow rate per lane? (b) What is the speed during peak-hour travel? (c) What is the density? (d) What is the weekday peak-hour level of service?

Answer: 1120 pcphpl, 67.88 mi/hr, 16 pc/mi-ln (pcpmpl), and B
Subdiscipline: transportation

An undivided suburban multilane highway segment with four 11 ft lanes (two in each direction) is used by weekday commuters. There is no median, and the two lanes in each direction are separated by a striped centerline. The estimated free-flow speed under ideal conditions is 60 mph. The segment contains 4% up- and downgrades 0.8 mi long. The fraction of recreational vehicles on this segment is essentially zero. However, the fraction of trucks is 10%. The lateral clearance on the right-hand side of the slow lane is 6 ft from the pavement edge. There is a 2 ft shoulder on each outside lane. There are no points of entry to the highway segment. (a) What is the hourly volume in the upgrade direction for LOS C? (b) What is the maximum capacity of the downgrade section? (c) What is the LOS in the downgrade section during the morning peak if the peak-hour traffic volume is 1300 vph?

Answer: 2390 pc/hr, 3798 pc/hr, and 12.9 pc/mi-lane
Subdiscipline: transportation

A signalized intersection, without pedestrian access and located in a central business district, has an approach with two 11 ft lanes on a 2% downgrade. 10% of the traffic consists of heavy trucks, but there are no buses or RVs. Both lanes are through lanes; no turns are permitted. There are no parking lanes. Arrivals to the intersection are random. What is the saturation flow rate of the approach?

Answer: 3140 pcphg