Practice Exam 1 AM (A) Solutions Practice Exam 1 AM (A) Practice Exam 1 AM (A) Solutions Q. 1 A storm drain inlet for a 2.7 acre parking area is to be designed. The rainfall intensity is 8.6 in/hr and the runoff coefficient is 0.96. The peak discharge, in cubic feet per second, is most nearly: (A) (B) (C) (D) 18 19 20 22 Solution Given: C = 0.96 I = 8.6 in/hr A = 2.7 acre Qp = C*I*A = 0.96*8.6*2.7 = 22.3 ft3/sec THE CORRECT ANSWER IS (D) Practice Exam 1 AM (A) Solutions Q. 2 The cantilevered retaining wall shown is under design. What is most nearly the active resultant per unit length of wall? 118.4lbf / ft 3 31o (A) (B) (C) (D) 280 lbf/ft 1900 lbf/ft 4260 lbf /ft 8530 lbf/ft Hint: Calculate the coefficient of active earth pressure and use it to find the active resultant. Solution The Rankine method may be used to find the active earth pressure acting at the base of the wall and granular backfill. Determine the active earth pressure acting at the base of the wall and then determine the active resultant. The equation for active pressure at the base of the wall is pa kav kaH The equation for the coefficient of active earth pressure is 1 sin 1 sin 31 ka 1 sin 1 sin 31 = 0.32 Calculate the resultant of the triangular pressure distribution. Ra 12 pa H 12 kaH 2 lbf 1 (0.32) 118.4 3 (15ft) 2 ft 2 = 4262 lbf/ft of wall length (4260 lbf/ft) Note that the resultant acts horizontally at the centroid of the triangular distribution at one third the height of the wall measured upward from the base. THE CORRECT ANSWER IS (C) Why Other Options Are Wrong Practice Exam 1 AM (A) Solutions (A) This solution fails to square the height of the wall in the resultant calculation. Note that the units are incorrect as well. (B) This incorrect solution assumes the active pressure acts at the centroid of the pressure distribution diagram; actually, it is the resultant active force that acts. This answer is obtained by multiplying by a centroid depth of 10 ft rather than 15 ft. (D) This solution fails to divide the result by two, as required by a triangular distribution. Q. 3 The maximum specific energy in a rectangular channel is 9 feet. The critical velocity, in ft/sec, is most nearly: (A) 8.7 (B) 12.3 (C) 14.1 (D) 15.4 Solution Solve for the critical depth, which will allow you to solve for the critical velocity. dc = 2/3 Ec = 2/3 * 9 = 6 feet vc = (gdc)1/2 = (32.2 * 6)1/2 = 13.9 ft /sec THE CORRECT ANSWER IS (C) Practice Exam 1 AM (A) Solutions Q. 4 A 10ft by 10ft square, reinforced concrete footing is installed so that the footing bearing surface is 5 ft below the soil level, at a point where the allowable soil pressure is 3500 psf. Other than the soil above the footing, there is no surcharge. The soil unit weight is 100 lbf/ft3. The footing is located at the corner of a building and is loaded through a concentric 14 in square column. The column transmits a 125,000 lbf service dead load and a 175,000 lbf service live load to the footing. The critical (plan) area contributing to two-way punching shear is assumed to be 92.44ft2.Th ede a dl oa di nc l ude st hec ol umn’ swe i g htbutdoe snoti nc l udet hef oot i ng’ swe i ght. The compressive strength for all of the concrete used is 3000 psi. The ultimate two-way punching shear, in lbf, is most nearly? (A) (B) (C) (D) 350,000 450,000 550,000 650,000 Solution The footing area is A B 2 (10 ft )(10 ft ) 100 ft 2 The ultimate load carried by the footing is P 1.4 Pd 1.7 Pl (1.4)(125, 000 lbf)+(1.7)(175,000 lbf) 472,500 lbf The factored soil pressure acting on the footing is P 472, 500 lbf pu u A 100 ft 2 4725 lbf/ft 2 The ultimate two-way punching shear is lbf Vu pu Acritical 4725 2 92.44ft 2 ft 436, 779 lbf THE CORRECT ANSWER IS (B) Practice Exam 1 AM (A) Solutions Q. 5 A 6.0 MGD water treatment plant is being planned that will use a local river as its water source. The raw water characteristics of the river are shown in Table 1. Tracer studies done on the disinfection tank of a drinking water treatment plant after construction produced the plot shown in the figure below. To satisfy the surface water treatment rule for disinfection of Giardia (Table 2) on a day when the peak hourly flow rate is 5 MGD, the water temperature is 10 C and the pH is 7.0, the residual chlorine concentration (mg/L) needed is most nearly: NOTE: The chlorine dosage must not exceed 1/8 mg/L to minimize THM formation. (A) 0.60 (B) 0.52 (C) 0.46 (D) 0.42 200 150 CONTACT TIME, t10 100 (min) 50 0 1 2 3 4 5 6 PEAK HOURLY FLOW RATE TABLE 1 Parameter Turbidity pH Alkalinity Calcium Temperature Value 17 NTU 6.8-7.1 S.U. 150 mg/L as CaCO3 51 mg/L as CaCO3 10 C to 26 C 7 Practice Exam 1 AM (A) Solutions TABLE 2 CT values (mg/L min) for inactivation of Giardia cysts by free chlorine at 10 C Chlorine Concentration (mg/L) 0.5 1.0 pH=7.0 Log Inactivations 1.5 2.0 2.5 3.0 18 33 33 70 82 105 0.4 19 38 56 75 94 113 0.6 20 40 59 79 99 119 0.8 21 41 62 82 103 123 1.0 21 42 64 85 106 127 1.2 22 44 65 87 109 131 1.4 22 45 67 89 112 134 1.6 23 46 68 91 114 137 1.8 23 46 70 93 116 139 2.0 24 47 71 95 118 142 2.2 24 48 72 96 120 144 2.4 24 49 73 97 122 146 2.6 25 49 74 99 123 148 2.8 25 50 75 100 125 150 3.0 Source: U.S. Environmental Protection Agency, Guidance Manual for Compliance with Filtration and Disinfection Requirements for Public Water Systems Using Surface Water Sources, Criteria and Standards Division, Office of Drinking Water (U.S.E.P.A. NTIS Publication NO. PB 90-148016), Washington, D.C: U.S. Government Printing Office, October, 1979. Solution Surface Water Treatment Rule for disinfection of Giardia; 3 log inactivation required. 2.5 log inactivation allowed for treatment prior to disinfection. Therefore, 3-2.5 = 0.5 log inactivation required by disinfection. From the figure, at a peak hourly flow rate of 5 MGD, t10 = 50 min contact time. CT 23 mg / L min; CT concentration x time Ref: Davis 7 Cornwell, Environmental Engineering, McGraw Hill, 1998, p. 244, Table 3-20. C = CT/T (23 mg / L min) / 50 min 0.46 mg / L residual chlorine concentration needed. THE CORRECT ANSWER IS: (C) Practice Exam 1 AM (A) Solutions Q. 6 An eight phase intersection looses 2 seconds per phase and has an all-red duration of 3 seconds on phases 1 and 4. If the sum of the ratios of approach flow to saturation flows for all phases is 0. 7( i . e .t hef l owt os a t ur a t i onf l owsf ora l lpha s e si s0. 7( i . e .t he" ΣY"va l ue ) ,t he nt heopt i mum cycle time, in seconds, is most nearly: (A) (B) (C) (D) 80 95 105 125 Solution 1 5 L 5 Co o 1 y i 1 where Co = optimum cycle time (sec) L = total lost time per cycle (sec) yi = maximum value of approach flows to saturation flows for all lane groups using phase i, qij/s; L i R i 1 2 8 2 3 = 22 sec (1.5 22) 5 Co 1 0.7 = 126.7 sec THE CORRECT ANSWER IS (D) Practice Exam 1 AM (A) Solutions Q. 7 I ft hede pt hoff l owi ngwa t e ri nadi t c hwi t hMa nni ng ’ sr oug hne s sof0. 02a nda na ve r a g ebe d slope of 0.5% is 2 feet, the velocity (fps) of the water would be most nearly: (A) 3.5 (B) 3.8 (C) 5.6 (D) 6.8 1 1 3 3 2' - 0" DITCH SECTION NOT TO SCALE Solution Determine the water velocity for the trapezoidal ditch. For a depth = 2.0 ft. A 2.0 3x2.0 2.0 16.0 ft 2 b zy y 2.0 3x2.0 2.0 1.092 ft R b 2 y 1 z 2 2.0 2x2.0 1 32 2 1 1.486 2 3 1 2 1.486 V R s x 1.092 3 0.005 2 5.6 ft / s n 0.02 THE CORRECT ANSWER IS: (C) Practice Exam 1 AM (A) Solutions Q. 8 Analyze the truss shown. h 2 h 2 The force in member AH is most nearly (A) (B) (C) (D) 300 lbf (compression) 600 lbf (compression) 670 lbf (compression) 670 lbf (tension) Hint: Solve by using the method of joints. Solution From the sum of the moments about E, the vertical reaction at support A is (300 lbf)(2h)+(200 lbf)(3h) RA,v 4h =300 lbf Draw the free-body diagram of joint A. By summing the forces in the horizontal direction, determine that the horizontal reaction at A is zero. The sum of the forces in the vertical direction is AH v RA,v 0 lbf Practice Exam 1 AM (A) Solutions AHv = 300 lbf (compression) From the geometry of the truss, the horizontal component of AH must be twice the vertical component. AHh = (2)(300 lbf) = 600 lbf (compression) The resultant force in member AH is AH AH v2 AH h2 (300 lbf) 2 600 lbf 2 = 670.8 lbf (670 lbf (compression)) THE CORRECT ANSWER IS (C) Why Other Options Are Wrong (A) This incorrect solution finds only the vertical component of the force in AH. (B) This incorrect solution finds the horizontal component of the force in AH. (D) This incorrect solution identifies the resultant force in AH as a tensile force. Practice Exam 1 AM (A) Solutions Q. 9 A city wants to design a sludge dewatering system for their 20-MGD secondary, activated sludge treatment plant shown below. The sludge volume reduction (%) achieved by the thickener is most nearly: (A) 50 (B) 58 (C) 65 (D) 70 BOD f =5mg/L TSS1 =200mg/L TSSPE =80mg/L TSSf =10mg/L 10, 000 lb/d@7500 Solution Assuming specific gravity of sludge is 1.00 Sludge quantity and volume to be dewatered. Primary Sludge lb / d (200 mg / L 80 mg / L)(8.34)(20 MGD ) 20, 016 lb / d 20, 016 lb / d gpd 68.571 gpd (8.34 lb / gal )(0.035) Secondary Sludge (was) 10, 000 lb / d gpd 0.1599 MGD 0.159,872 gpd (8.34 lb / gal )(7,500 mg / L) Before Thickening Total quantity = 20, 016 10, 000 30, 016 lb / d Total volume = 68,571+159,872 = 228,443 gpd Practice Exam 1 AM (A) Solutions After Thickening Total quantity = 30,016 lb/d Total volume 30, 016 79,979 gpd (8.34 lb / gal )(0.045 percentage) % R eduction in sludge volume= CORRECT ANSWER IS: (C) 228.443-79,979 65% 228.443 Practice Exam 1 AM (A) Solutions Q. 10 Groundwater monitoring wells have been installed at the site of a proposed sanitary landfill such that Well B is located 1,500 feet north and 300 feet west of Well A. A proposed containment cell, having bottom dimensions of 500 feet (north to south) and 100 feet (east to west), is to be located such that the southeast corner is 100 feet west and 500 feet north of Well A. The bottom of the landfill cell must be a minimum of 5 feet above the groundwater elevation. The elevations that were determined at each well location are shown in the table below. The minimum bottom elevation for the proposed landfill cell if the bottom is to be level is most nearly: (A) 227 (B) 232 (C) 237 (D) 242 Well A B Groundwater Elevation(ft) 229.75 222.25 Ground Surface Elevation (ft) 248.75 243.75 Solution Determine minimum bottom elevation of the containment cell. The highest groundwater elevation within cell area = groundwater elevation at point A less the groundwater drop to closest point of the cell, Point C highest groundwater elevation within cell area = groundwater elevation at Point A less the (distance A to C)*I Distance Well A to cell [(500) *(500) (100)*(100)0.5 ] 510 ft Highest groundwater elevation within cell area 229.75 510* 0.0049 227.25 Minimum bottom elevation of containment cell = highest groundwater elevation within cell area plus 5 feet = 227.25 + 5 feet Minimum bottom elevation of containment cell = 232 feet CORRECT ANSWER IS: (B) Practice Exam 1 AM (A) Solutions Q 11 A soil sample, taken from a borrow pit has a specific gravity of soil solids of 2.66. The sample was taken to a materials laboratory and tested. The results of a standard Proctor test are tabulated below. Weight of soil (lb) Moisture content (%) 3.20 12.8% 3.78 13.9% 4.40 15.0% 4.10 15.7% 3.70 16.6% 3.30 18.1% The maximum dry density, in lb/ft3, is most nearly: (A) 85 (B) 90 (C) 100 (D) 115 Solution Step 1: Derive unit weight (of wet soil) from: = weight of soil/volume of proctor mold, where volume of proctor mold = 1/30 ft3. Weight Moist unit of soil weight lb lb/ft3 W 3.2 96 3.8 113 4.4 132 4.1 123 3.7 111 3.3 99 Practice Exam 1 AM (A) Solutions Step 2: Derive dry density d d / (1+w) Moist unitMoisture Dry weight content density lb/ft3 % lb/ft3 w d 96 11% 86 113 13% 100 132 15% 115 123 17% 105 111 18% 94 99 19% 83 Step 3: Plot Moisture content (w) vs dry density ( d) 115 110 Dry unit weight, d (lb/ft3) 120 105 100 95 90 85 80 10% 12% 14% 16% 18% 20% Moisture Content, w (% ) Step 4: Identify maximum dry density ( d) and optimum moisture content (w) from the plot: Optimum moisture content = w = 15% and d(max) = 115 pcf THE CORRECT ANSWER IS (D) Practice Exam 1 AM (A) Solutions Q. 12 A horizontal curve for a section of a highway has a design speed of 60 mph. The terrain restricts the radius of the curve to 1200 ft, which therefore requires the super elevation at the curve, in percent, to be most nearly: (A) 4 (B) 6 (C) 8 (D) 10 Solution u2 Radius ( ft ) 15(e f s ) Given the radius of 1200 feet and the design speed of 60 mph, the side friction factor (fs) comes from Exhibit 3-14onpa ge145oft he2001AASHTO“ APol i c yonGe ome t r i cDe s i g nof Hi g hwa y sa ndSt r e e t s ”whi c hi sba s e dont hede s i g ns pe e d.I ti ndi c a t e st ha tf ora60mphde s i g n speed the side friction factor is 0.12 fs = 0.12 Substituting the known values into the radius equation, the only unknown is the super elevation, e. By solving for e, the super elevation rate is found. (60mph) 2 1200 ft 15(e 0.12) 602 3600 e 0.12 e 0.12 0.08 8% 1200(15) 1200(15) THE CORRECT ANSWER IS ( C ) Practice Exam 1 AM (A) Solutions Q. 13 A horizontal curve is defined by its radius of 851 feet, as shown below. The length of the chord AB, in feet, is most nearly: A B 12% 36o (A) (B) (C) (D) 505 515 525 535 Solution The chord is the straight-line distance from A to B. AD sin 36 2 AO AD C / 2 Practice Exam 1 AM (A) Solutions AO R 851 C 2(851)sin(18) 525.95 Arc ACB= 2851 534.70 360 THE CORRECT ANSWER IS (C) Q. 14 A concrete column and footing caries the loads shown. The footing is 6 ft wide. column dead load column live load moment due to wind compressive strength of concrete maximum allowable soil pressure 80 kips 100 kips 50 ft-kips 3000 lbf/in2 3000 lbf/in2 What is the minimum footing length, L, required for the entire footing to be considered effective in carrying these loads? (A) (B) (C) (D) 1.7 ft 1.8 ft 7.7 ft 10 ft Hint: For the entire footing to be effective, avoid tensile stress in the soil. Practice Exam 1 AM (A) Solutions Solution Limit eccentricity, e, to one-sixth of the footing length to keep the soil resultant within the kern limit and avoid tension in the soil. M M e wind P PD PL 50 ft kips 80 kips 100 kips = 0.28 ft L e 6 L 0.28 ft 6 Solving for L, L 0.28 ft 6 1.68 ft 1.7 ft THE CORRECT ANSWER IS (A) Why Other Options Are Wrong (B) This incorrect solution calculates eccentricity using factored loads. Factored loads are used in concrete design, but not for determining footing size. Footing size should be based on unfactored soil pressure. (C) This incorrect solution calculates the required size of a square footing (ignoring the footing width given) based on the dead and live loads and allowable soil pressure. The problem statement is asking for the minimum length required for the entire footing to be effective, not the minimum size based on the soil pressure. (D) This incorrect solution calculates the required length based on the dead and live loads and allowable soil pressure. The problem statement is asking for the minimum length required for the entire footing to be effective, not the minimum size based on the soil pressure. Practice Exam 1 AM (A) Solutions Q. 15 The mechanical and plasticity tests of a soil under consideration as a fill material are shown below: A soil is under investigation. Mechanical and plasticity test results are shown below: Mechanical Analysis Sieve % passing by weight 10 19 40 25 200 66 Plasticity Liquid Limit Plastic Limit 40 20 The soil may be classified, according to the Unified Soil Classification (USCS) system as: (A) (B) (C) (D) GP SW CL CH Solution Refer to the Unified Soil Classification System, Technical Memorandum No. 3-357, US Army Engineers Waterways Experiment Station, Vicksburg, Mississippi, 1960. Note, this classification table is reproduced in most geotechnical textbooks. You will find it typically titled a s“ TheUni f i e dSoi lCl a s s i f i c a t i onSy s t e m” . The Unified Soil Classification system has two analytical components: 1. Particle size 2. Plasticity Particle size Less than half of the material is larger than No. 200 sieve: the material is a Fine-grained soil. Plasticity TheAt t e r be r g ’ spl oti sa bovet he“ A”l i ne ,a ndt hePIi sg r e a t e rt ha n7,t heg r oups y mboli sCL. The soil can be classified as CL –Silty Clay. THE CORRECT ANSWER IS (C) Practice Exam 1 AM (A) Solutions Q. 16 A transition curve is to be used to implement a change in cross-section from a normally crowned section to a fully superelevated section. The outer lane is to be gradually aligned from the normally crowned section to a straight level section at the Tangent-to-Spiral (T.S.) point. The full superelevation is rotated about the centerline. Degree of Curve (D) = 2.5° Two 11-foot lanes Design superelevation = 0.08 ft/ft Grade = +1.50% Crown = 0.015 ft/ft T.S. Station = 100 + 00.00 T.S. CL Elevation = 2,500.00 ft. Length of spiral = 230 ft The station (feet) where full superelevation is reached is most nearly: (A) 100 + 00 (B) 100 + 25 (C) 101 + 00 (D) 102 + 50 Solution S.C. Sta. = T.S. Sta. + LS = (100+00) + (2 + 30) = 102 + 30 THE CORRECT ANSWER IS: (D) Practice Exam 1 AM (A) Solutions Q. 17 Using the NDS, which of the following statements must be true? I. The temperature factor, Ct, applies to member subjected to extremely cold temperatures. II. The volume factor, CV, applies only to glued laminated timber bending members. III. The bending design value, Fb, for a floor framed with 1 x 6 sawn lumber joists must be multiplied by the repetitive member factor. IV. The load duration factor, CD, does not apply to the modulus of elasticity values. (A) (B) (C) (D) I and II II and III II and IV III and IV Hint: Refer to NDS Sec 2.3 for adjustment of design values. Solution Section 2.3 and Table 2.3.1 of the NDS contain the adjustment factors and their applicability for design values. The volume factor, CV, is discussed in the footnotes to NDS Table 2.3.1. Footnote 3 states, "The volume factor, CV, shall apply only to glued laminated timber bending members (see Sec. 5.3.2)." Statement II is true. The load duration factor, CD, is discussed in NDS sec. 2.3.2 and NDS table 2.3.2. Both NDS Sec. 2.3.2.1 and Footnote 1 to NDS Table 2.3.2 state that "Load duration factors shall not apply t omodul usofe l a s t i c i t y ,E…"St a t e me ntI Vi st r ue . THE CORRECT ANSWER IS (C) Why Other Options Are Wrong (A) Although statement II is true, statement I is false. The temperature factor, Ct, is discussed in NDS Sec. 2.3.4. The temperature factor applies to members subjected to sustained exposure to elevated (over 100 F) temperatures. Because the statement applies to members subjected to extreme cold, not heat, statement I is false. (B) Although statement II is true, statement III is false. The repetitive member factor, Cr, is discussed in Footnote 5 of NDS Table 2.3.1 Footnote 5 states, "The repetitive member factor, Cr, shall apply only to dimension lumber bending members 2 in to 4 in thick (see Sec. 4.3.4)." Because the joists in this case are 1 in thick, statement III is false. (D) Although statement IV is true, statement III is false because the repetitive member factor, Cr, applies only to dimension lumber bending members 2 in to 4 in thick. The joists in this case are 1 in thick. Practice Exam 1 AM (A) Solutions Q.-18 A soil sample weighing 66.8 lb with a moisture content of 19 percent, volume of 0.55 cubic feet, has a specific gravity of 2.72. The degree of saturation is most nearly: (A) (B) (C) (D) 0.5 0.6 0.7 0.8 Solution W / V = 66.83 / 0.55 = 121.5 pcf d / (1 + w) d = 121.5 / (1 + 0.19) d = 102.1 pcf d = (Gs * w ) / (1 + e) e = ((Gs * w ) / d ) –1 e = ((2.72 * 62.4) / 102.1) –1 e = 0.66 S = (w * Gs) / e S = ((0.19)*(2.72)) / 0.66 S = 0.78 THE CORRECT ANSWER IS: (D) Practice Exam 1 AM (A) Solutions Q. 19 What is the average hydraulic detention time for a rectangular tank with dimensions of 2.5 m by 15 m by 3.0 m deep receiving a flow of 900 m3/d? The hydraulic efficiency of the tank is 83%. (A) (B) (C) (D) 2.3 h 2.5 h 3.0 h 3.6 h Hint: The average detention time will be less than the theoretical detention time. Solution E Q t ta V fractional efficiency flow rate theoretical hydraulic detention time actual hydraulic detention time volume m3/d d d m3 h (2.5m)(15m)(3.0m) 24 V d t 3 m Q 900 d 3.0 h ta tE 83% 3.0 h 100% =2.5 h THE CORRECT ANSWER IS (B) Why Other Options Are Wrong (A) This incorrect solution divides the flow rate by the volume to get the theoretical detention time. The theoretical detention time is then divided by the percent efficiency instead of being multiplied by the fractional efficiency. Other definitions and equations are unchanged from the correct solution. m3 h 900 24 d Q d t V 2.5m)(15m)(3.0m 192 h/d 2 h 192 2 ta d 83% 2.3 h Units do not make sense. Practice Exam 1 AM (A) Solutions (C) This incorrect solution calculates the theoretical detention time. The hydraulic efficiency is ignored. Other definitions and equations are unchanged from the correct solution. h 2.5m)(15m)(3.0m 24 d t 3 m 900 d 3.0 h (D) In this incorrect solution, the theoretical detention time is divided by the hydraulic efficiency instead of being multiplied by it. Other definitions and equations are unchanged from the correct solution. h 2.5m)(15m)(3.0m 24 d t 3 m 900 d 3.0 h 100% ta 3.0 h 83% =3.6 h Q. 20 Assume all soils in a drainage basin are in the Soil Conservation Service (SCS) hydrologic soil Group B. Also assume that the vegetative covers are in good condition. The land use is parks and open space. The SCS Runoff Curve Number (CN) for the entire area is most closely approximated by: (A) 43 (B) 54 (C) 61 (D) 81 Solution Determine the SCS Runnoff Curve Number for the entire area. For soil Group B, with good vegetative cover in urban, fully developed open space (parks, lawns), the appropriate SCS curve number (Gupta, Hydrology and Hydraulic Systems, Prentice Hall, 1989, p. 101) CN = 61 THE CORRECT ANSWER IS (C)
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