FE CIVIL – FIFTH SIMULATION

#1. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=320 in^4, span L=312 in. Compute midspan deflection δ=PL^3/(48EI).

1.6364 in

4.9092 in

0.5455 in

0.0008 in

#2. Using Greenshields model v=vf(1-k/kj), maximum flow occurs at k=kj/2. For vf=55 mph and kj=180 veh/mi/ln, what is qmax?

2475 veh/h/ln

9900 veh/h/ln

90 veh/h/ln

1237.5 veh/h/ln

#3. A fully restrained steel member has E=204 GPa, α=1.1e-05 /°C, and temperature rise ΔT=105°C. What thermal stress develops (σ=EαΔT)?

235.62 MPa (compression)

2356.2 MPa (compression)

2.24 MPa (compression)

12.71 MPa

#4. A concrete design uses water=204 kg/m^3, w/c=0.4, and cement specific gravity=3.2. What is the absolute volume of cement in 1 m^3 of concrete?

0.1992 m^3

0.51 m^3

0.1195 m^3

0.1594 m^3

#5. Given specific gravity Gs=2.75, water content w=20%, and void ratio e=0.7, compute degree of saturation Sr=wGs/e.

78.57%

32.73%

7.86%

21.43%

#6. For earthwork, cross-sectional areas are A1=2113, Am=1278, A2=2527 ft^2 over spacing L=177 ft. What volume by prismoidal formula?

10654.963 ft^3

410640 ft^3

287684 ft^3

349162 ft^3

#7. For a reinforced concrete beam, As=4.0 in^2, fy=75 ksi, d=20 in, a=2.5 in. Compute design moment φMn with Mn=Asfy(d-a/2), φ=0.9.

354.3792 kip-ft

421.88 kip-ft

527.34 kip-ft

468.75 kip-ft

#8. Which method is commonly used to solve elementary statically indeterminate beams by compatibility and superposition?

Force method (consistent deformations)

Direct stiffness prohibited for indeterminate systems

Method of joints only

Rankine earth-pressure method

#9. A rehabilitation program costs $13000 at year-end for 5 years. At interest rate 6%, what is the present worth?

$54760.73

$216666.67

$65000

$62974.84

#10. A plane truss has m=23 members, j=16 joints, r=5 reaction components. What is degree of static indeterminacy m+r-2j?

-4

4

5

-2

#11. A particle starts with speed 8 ft/s and constant acceleration 2 ft/s^2 over displacement 168 ft. Using v^2=v0^2+2as, what is final speed?

0 ft/s

736 ft/s

27.13 ft/s

344 ft/s

#12. A rehabilitation program costs $23000 at year-end for 7 years. At interest rate 9%, what is the present worth?

$133121.6

$161000

$255555.56

$115757.92

#13. CPM network has two parallel paths from start to finish: Path 1 durations 6 and 6 days; Path 2 durations 4 and 6 days. What is project duration?

10 days

14 days

12 days

22 days

#14. Two retaining-wall faces are modeled by parallel lines 5x + 4y + (-14) = 0 and 5x + 4y + 13 = 0, with coordinates in ft. What is the perpendicular separation between the faces?

2.11 ft

27 ft

4.22 ft

19.09 ft

#15. A concrete design uses water=163 kg/m^3, w/c=0.5, and cement specific gravity=3.1. What is the absolute volume of cement in 1 m^3 of concrete?

0.326 m^3

0.0789 m^3

0.1052 m^3

0.1315 m^3

#16. At status date: BAC=$1,200,000, EV=$420,000, AC=$610,000. Assume future cost performance follows current CPI. Using EAC=BAC/CPI, what is estimate at completion?

$2004285.71

$1390000

$826229.51

$1742857.14

#17. Coordinates of a triangular lot are (1261,2910), (1688,2910), (1360,3099) ft. What is the area by coordinate method?

200.88 ft^2

40351.5 ft^2

20175.75 ft^2

80703 ft^2

#18. A signalized intersection has heavy left-turn demand causing spillback. Which control strategy is most direct for reducing opposing-flow conflicts and delay?

Use stop control on all approaches simultaneously

Remove all left-turn lanes

Increase posted speed through intersection

Provide protected left-turn phasing with optimized cycle split

#19. In Hardy Cross analysis of looped distribution systems, what condition must be satisfied at convergence for each loop?

Velocity in every pipe segment is the same

Algebraic sum of head losses around each closed loop equals zero

All nodal pressures are identical

Flow direction in each loop must be clockwise

#20. An asphalt overlay covers 560 m × 22 m at compacted thickness 0.25 m. Use mix density 2500 kg/m^3 and supply+place cost $95/metric ton. What is estimated cost?

$950950

$7700

$562692.31

$731500

#21. For stress state σx=111 MPa, σy=-16 MPa, τxy=36 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

63.5 MPa

47.5 MPa

127 MPa

72.99 MPa

#22. A detention pond outlet is redesigned to reduce post-development peak flow to pre-development levels. Which principle is most directly applied?

Immediate bypass of all stormwater to downstream channel

Temporary storage with controlled release to attenuate peak discharge

Increasing impervious area to shorten time of concentration

Permanent abstraction of all runoff volume

#23. A flood-mitigation project provides immediate present-value benefits of $338000. Initial cost is $153000 plus annual O&M of $17000 for 9 years at 7%. What is the benefit-cost ratio?

0.281

1.631

1.281

0.78

#24. Flow in a reducer has D1=0.5 m, D2=0.15 m, and upstream velocity V1=1.2 m/s. By continuity, what is V2?

20 m/s

6.667 m/s

0.108 m/s

13.333 m/s

#25. A geotechnical alert model flags instability (event B). Prior probability of true instability A is 0.2. Sensitivity P(B|A)=0.7, false-positive rate P(B|not A)=0.1. What is P(A|B)?

0.6364

0.6

0.22

0.3636

#26. Coordinates of a triangular lot are (1778,1295), (2226,1295), (2063,1540) ft. What is the area by coordinate method?

109760 ft^2

234.26 ft^2

27440 ft^2

54880 ft^2

#27. For crest vertical curve design with grade change A=6.0%, choose K=48.67 from SSD criteria (given). What curve length L=KA is required?

146 ft

8.1 ft

292 ft

438 ft

#28. A particle starts with speed 24 ft/s and constant acceleration 1 ft/s^2 over displacement 69 ft. Using v^2=v0^2+2as, what is final speed?

26.72 ft/s

93 ft/s

20.93 ft/s

714 ft/s

#29. A contract has original value $2,420,000 and approved change orders $165,000. Previous paid progress was 45% of current contract value; this month total earned reaches 68%. With 5% retainage on current earnings, what payment is due this month?

$474450.9

$1669910

$564822.5

$594550

#30. A bid has direct costs: labor $180,000, equipment $95,000, materials $330,000, subcontracts $160,000. Apply bond 1.0%, overhead 8%, and fee 10% to direct cost. What is total bid?

$902700

$910350

$918000

$765000

#31. A steel member (α=6.5e-06/°F) is 60 ft long and heats by 99°F. What free thermal expansion occurs?

0.4633 ft

0.0386 ft

0.0032 ft

0.0006 ft

#32. Traverse has two legs: 287 m at azimuth 57°, then 373 m at azimuth 145°. What is straight-line distance from start to end?

86 m

478.51 m

382.81 m

660 m

#33. Using LRFD combo U=1.2D+1.6L+0.5W with D=61 kip, L=36 kip, W=40 kip, what is factored load U?

146.6 kip

137 kip

150.8 kip

130.8 kip

#34. A rectangular plate 7m×8m has a centered rectangular hole 5m×5m. What is ȳ from the base?

1.5 m

3.54 m

4 m

5.21 m

#35. In slope stability analyses, increasing positive pore-water pressure along a potential slip surface generally causes what effect?

Decreases effective normal stress and reduces factor of safety

No influence on strength parameters

Increases shear strength through higher effective stress

Always increases apparent cohesion

#36. For the circle (x–1)^2 + (y-4)^2 = 81 and the line y = -0.5x + 12.67, how many real intersection points are there?

0

2

Infinite

1

#37. For a rectangle b=12 in, h=12 in, find I_x about an axis parallel to centroidal x-axis and offset by d=4 in using parallel-axis theorem.

1744 in^4

2304 in^4

4032 in^4

1728 in^4

#38. Using NRCS runoff method: for storm P=3.0 in and curve number CN=85, compute runoff depth Q (in).

0.556 in

2.224 in

1.412 in

1.588 in

#39. A circular shaft transmits torque T=5000 N·mm. At radius r=33 mm with polar moment J=200000 mm^4, what is torsional shear stress τ=Tr/J?

27.225 MPa

0.825 MPa

0.0008 MPa

1.2121 MPa

#40. A concrete design uses water=161 kg/m^3, w/c=0.45, and cement specific gravity=3.2. What is the absolute volume of cement in 1 m^3 of concrete?

0.0839 m^3

0.1118 m^3

0.3578 m^3

0.1398 m^3

#41. Flow in a reducer has D1=0.4 m, D2=0.15 m, and upstream velocity V1=1.2 m/s. By continuity, what is V2?

0.169 m/s

12.8 m/s

4.267 m/s

8.533 m/s

#42. In the four-step travel demand model, where are origin-destination movements between zones estimated?

Trip generation only

Trip distribution step

Traffic assignment only

Mode choice calibration only

#43. Lime stabilization of clayey subgrade is primarily used to achieve which combined effect?

Increase organic content for compressibility

Eliminate need for moisture-density control

Reduce plasticity and swell potential while improving strength/workability

Create fully impermeable layer regardless compaction

#44. A sediment basin excavation covers 6.2 acres to average depth 2.0 ft. A dozer spread has nominal output 900 yd^3/day with site efficiency 0.75. How many full days are required (ignore weather)?

28 days

30 days

32 days

22.23 days

#45. For stress state σx=61 MPa, σy=-43 MPa, τxy=39 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

52 MPa

65 MPa

104 MPa

9 MPa

#46. In Hardy Cross analysis of looped distribution systems, what condition must be satisfied at convergence for each loop?

Flow direction in each loop must be clockwise

All nodal pressures are identical

Algebraic sum of head losses around each closed loop equals zero

Velocity in every pipe segment is the same

#47. A unit-price contract has a bid item quantity underrun. Original amount is $74200. A signed change order adds $6100 for additional dewatering. What is the revised contract amount?

$86400

$80300

$68100

$74200

#48. A simply supported beam span 16 ft has full-span UDL w=6 kip/ft plus point load P=12 kip at x=11 ft from left. What is the maximum positive bending moment (approx., governing critical section)?

223.17 kip-ft

900 kip-ft

216 kip-ft

240 kip-ft

#49. A 21 kg cart increases speed from 5 m/s to 14 m/s on level track. Neglecting losses, what net work is required?

850.5 J

-1795.5 J

1795.5 J

189 J

#50. For c=0 strip footing approximation qult=γDfNq+0.5γBNγ. Given γ=17, Df=2.0 m, B=1.5 m, Nq=22, Nγ=20, find qult.

1003 kPa

34 kPa

3009 kPa

334.33 kPa

#51. Direct shear test interpretation gives c=18 kPa and φ=28°. At normal stress 80 kPa, what peak shear stress is predicted?

42.54 kPa

37.56 kPa

78.7 kPa

60.54 kPa

#52. A plane truss has m=30 members, j=18 joints, r=3 reaction components. What is degree of static indeterminacy m+r-2j?

4

3

-3

-1

#53. An asphalt overlay covers 420 m × 26 m at compacted thickness 0.3 m. Use mix density 2400 kg/m^3 and supply+place cost $125/metric ton. What is estimated cost?

$982800

$7862.4

$1277640

$756000

#54. Two coplanar forces act at a point: F1 = 14 lb at 54° from +x and F2 = 10 lb at 138° from +x. What is resultant magnitude?

18.04 lb

21.64 lb

4 lb

24 lb

#55. A steel tension member has gross area Ag=10.0 in^2 and Fy=65 ksi. If yielding controls with φ=0.9, what is design strength φPn?

702 kip

650 kip

491.4 kip

585 kip

#56. Lime stabilization of clayey subgrade is primarily used to achieve which combined effect?

Reduce plasticity and swell potential while improving strength/workability

Create fully impermeable layer regardless compaction

Increase organic content for compressibility

Eliminate need for moisture-density control

#57. A triangular construction lot has vertices at (0,0), (14,3), and (4,13) in a Cartesian site grid measured in m. Using the shoelace method, what is the lot area?

170 m^2

42.5 m^2

85 m^2

182 m^2

#58. Between two points in water system: p1=180 kPa, z1=102.0 m, V1=1.2 m/s; p2=80 kPa, z2=100.0 m, V2=2.0 m/s; headloss=2.5 m. Required pump head?

-0.53 m

5.53 m

-1.97 m

0.53 m

#59. Simply supported beam L=36 ft has UDL w=1.2 kip/ft plus point load P=10 kip at a=12 ft from left. What is governing positive moment (critical section approximation)?

332.92 kip-ft

432.79 kip-ft

284.4 kip-ft

239.4 kip-ft

#60. A force with components Fx = -19 lb, Fy = 17 lb is applied at position (x, y)=(8, 2) ft from O. What is scalar moment M_O = xFy – yFx?

-20 lb-ft

174 lb-ft

98 lb-ft

121.8 lb-ft

#61. A consultant deviates from accepted pavement testing standards and the owner incurs $297000 in corrective work. Which legal theory most directly supports owner recovery?

Strict criminal liability without proof of breach

Professional negligence based on breach of the standard of care

Force majeure because testing involved uncertainty

Unjust enrichment regardless of professional duty

#62. Direct shear test interpretation gives c=8 kPa and φ=28°. At normal stress 80 kPa, what peak shear stress is predicted?

65.7 kPa

37.56 kPa

50.54 kPa

42.54 kPa

#63. Lines 3x + 1y = -15 and 2x + (-4)y = 12 intersect at P. What is the equation of the line through P that is perpendicular to y = 3x + 1?

y = -0.33x + -5.86

y = 0.33x + 5.86

y = 3x + 5.86

y = -0.33x + 5.86

#64. Two coplanar forces act at a point: F1 = 20 N at 50° from +x and F2 = 15 N at 129° from +x. What is resultant magnitude?

35 N

32.63 N

27.19 N

5 N

#65. A slender rod of mass 9 kg and length 6 m rotates about its centroidal axis perpendicular to the rod. What is mass moment of inertia?

54 kg·m^2

162 kg·m^2

27 kg·m^2

108 kg·m^2

#66. A unit-price contract has a bid item quantity underrun. Original amount is $71800. A signed change order adds $6200 for additional dewatering. What is the revised contract amount?

$65600

$84200

$71800

$78000

#67. A project has three mutually exclusive outcomes: high gain $218000 with probability 30%, moderate gain $124000 with probability 10%, and loss $127000 otherwise. What is expected value?

$154000

$1120

$91000

$1600

#68. A unit-price contract has a bid item quantity underrun. Original amount is $57000. A signed change order adds $10000 for additional dewatering. What is the revised contract amount?

$47000

$67000

$57000

$77000

#69. For stress state σx=164 MPa, σy=-34 MPa, τxy=87 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

99 MPa

131.8 MPa

65 MPa

198 MPa

#70. A signalized intersection has heavy left-turn demand causing spillback. Which control strategy is most direct for reducing opposing-flow conflicts and delay?

Use stop control on all approaches simultaneously

Increase posted speed through intersection

Remove all left-turn lanes

Provide protected left-turn phasing with optimized cycle split

#71. Using NRCS runoff method: for storm P=3.5 in and curve number CN=75, compute runoff depth Q (in).

0.415 in

1.302 in

1.823 in

2.198 in

#72. Differential leveling run: BM elev=242 ft; BS1=6.37 ft, FS1=4.83 ft, BS2=3.02 ft, FS2=4.83 ft. What is ending elevation?

242.28 ft

261.05 ft

241.72 ft

246.72 ft

#73. A fine-grained soil plots above the A-line with LL=62 and PI=34. Under USCS, what classification is most likely?

ML

CL

SM

CH (high-plasticity clay)

#74. A flood-mitigation project provides immediate present-value benefits of $360000. Initial cost is $340000 plus annual O&M of $12000 for 8 years at 6%. What is the benefit-cost ratio?

-0.132

1.151

1.218

0.868

#75. Material test results occur at values 13, 35, and 47 MPa with frequencies 7, 10, and 6. What is the weighted mean strength?

32.86 MPa

47 MPa

31.43 MPa

31.67 MPa

#76. Coordinates of a triangular lot are (1633,1719), (1972,1719), (1749,1926) ft. What is the area by coordinate method?

70173 ft^2

187.31 ft^2

17543.25 ft^2

35086.5 ft^2

#77. Between two points in water system: p1=220 kPa, z1=110.0 m, V1=1.8 m/s; p2=60 kPa, z2=95.0 m, V2=2.0 m/s; headloss=3.5 m. Required pump head?

-6.621 m

-11.621 m

11.621 m

-15.121 m

#78. Flow in a reducer has D1=0.4 m, D2=0.25 m, and upstream velocity V1=1.8 m/s. By continuity, what is V2?

2.304 m/s

4.608 m/s

6.912 m/s

0.703 m/s

#79. Using Greenshields model v=vf(1-k/kj), maximum flow occurs at k=kj/2. For vf=55 mph and kj=180 veh/mi/ln, what is qmax?

2475 veh/h/ln

90 veh/h/ln

9900 veh/h/ln

1237.5 veh/h/ln

#80. A circular sewer flows full with D=0.6 m, slope S=0.002, Manning n=0.013. Estimate capacity Q using Manning equation.

0.0006 m^3/s

0.2746 m^3/s

0.4119 m^3/s

0.1373 m^3/s

#81. Differential leveling run: BM elev=358 ft; BS1=5.06 ft, FS1=4.98 ft, BS2=3.68 ft, FS2=5.51 ft. What is ending elevation?

359.76 ft

377.22 ft

356.24 ft

361.24 ft

#82. Traverse has two legs: 568 m at azimuth 60°, then 204 m at azimuth 121°. What is straight-line distance from start to end?

690.36 m

364 m

552.28 m

772 m

#83. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=240 in^4, span L=264 in. Compute midspan deflection δ=PL^3/(48EI).

1.3218 in

3.9655 in

0.4406 in

0.0009 in

#84. In slope stability analyses, increasing positive pore-water pressure along a potential slip surface generally causes what effect?

No influence on strength parameters

Always increases apparent cohesion

Increases shear strength through higher effective stress

Decreases effective normal stress and reduces factor of safety

#85. A plane truss has m=20 members, j=16 joints, r=6 reaction components. What is degree of static indeterminacy m+r-2j?

7

-6

6

-4

#86. A fully restrained steel member has E=201 GPa, α=1.1e-05 /°C, and temperature rise ΔT=120°C. What thermal stress develops (σ=EαΔT)?

13.2 MPa

265.32 MPa (compression)

2653.2 MPa (compression)

2.21 MPa (compression)

#87. Direct shear test interpretation gives c=12 kPa and φ=28°. At normal stress 140 kPa, what peak shear stress is predicted?

65.73 kPa

112.37 kPa

74.44 kPa

86.44 kPa

#88. A simply supported beam span 23 ft carries a uniform load w=2 kip/ft over full span and a point load P=15 kip at 13 ft from A. Find reaction at B.

8.48 kip

30.5 kip

29.52 kip

31.48 kip

#89. In Hardy Cross analysis of looped distribution systems, what condition must be satisfied at convergence for each loop?

All nodal pressures are identical

Flow direction in each loop must be clockwise

Algebraic sum of head losses around each closed loop equals zero

Velocity in every pipe segment is the same

#90. A force with components Fx = 12 lb, Fy = -8 lb is applied at position (x, y)=(6, 6) ft from O. What is scalar moment M_O = xFy – yFx?

-120 lb-ft

120 lb-ft

48 lb-ft

24 lb-ft

#91. Flow in a reducer has D1=0.5 m, D2=0.25 m, and upstream velocity V1=1.8 m/s. By continuity, what is V2?

10.8 m/s

3.6 m/s

7.2 m/s

0.45 m/s

#92. Which method is commonly used to solve elementary statically indeterminate beams by compatibility and superposition?

Method of joints only

Direct stiffness prohibited for indeterminate systems

Rankine earth-pressure method

Force method (consistent deformations)

#93. A plane truss has m=29 members, j=13 joints, r=5 reaction components. What is degree of static indeterminacy m+r-2j?

-8

8

9

10

#94. For the circle (x–4)^2 + (y-4)^2 = 25 and the line y = -0.5x + -4.71, how many real intersection points are there?

1

2

Infinite

0

#95. Water at 20°C has ν=1.1e-06 m^2/s in a pipe with V=1.2 m/s and D=0.1 m. What Reynolds number Re=VD/ν?

109091

10909

1090909

10909091

#96. A simply supported beam span 13 m carries a uniform load w=8 kN/m over full span and a point load P=14 kN at 2 m from A. Find reaction at B.

63.85 kN

59 kN

54.15 kN

2.15 kN

#97. A steel member (α=5.5e-06/°F) is 67 ft long and heats by 88°F. What free thermal expansion occurs?

0.0324 ft

0.3891 ft

0.0005 ft

0.0027 ft

#98. A block of weight 440 N is on a 20° incline with μs=0.3. What minimum force parallel to plane is required to start moving it up the incline?

274.53 N

132 N

413.46 N

26.45 N

#99. A design penalty function is C(x) = 3x + 139/x + 7 for x>0. At what x is C(x) minimized?

46.33

0.15

6.81

3.59

#100. Water at 20°C has ν=1.3e-06 m^2/s in a pipe with V=2.0 m/s and D=0.05 m. What Reynolds number Re=VD/ν?

30769231

76923

7692

769231

#101. For crest vertical curve design with grade change A=7.0%, choose K=59 from SSD criteria (given). What curve length L=KA is required?

8.4 ft

413 ft

619.5 ft

206.5 ft

#102. For a rectangle b=12 in, h=12 in, find I_x about an axis parallel to centroidal x-axis and offset by d=4 in using parallel-axis theorem.

1728 in^4

4032 in^4

2304 in^4

1744 in^4

#103. A stream shows elevated BOD and low dissolved oxygen in warm weather. Which interpretation is most defensible?

High biodegradable loading can increase oxygen consumption and depress DO, especially at higher temperatures

Higher BOD always increases dissolved oxygen

Only pH controls oxygen depletion in natural waters

DO is independent of temperature and biological activity

#104. Using AASHTO-style SN=a1D1+a2m2D2+a3m3D3, with SN=4.8, a1=0.44, D1=5.0 in, a2=0.14, m2=1.0, and ignoring D3, what base thickness D2 is needed?

26 in

34.29 in

18.57 in

11.14 in

#105. For stress state σx=53 MPa, σy=88 MPa, τxy=57 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

59.63 MPa

70.5 MPa

35 MPa

-17.5 MPa

#106. Using NRCS runoff method: for storm P=3.0 in and curve number CN=75, compute runoff depth Q (in).

0.961 in

2.039 in

1.345 in

0.368 in

#107. At status date: BAC=$950,000, EV=$420,000, AC=$460,000. Assume future cost performance follows current CPI. Using EAC=BAC/CPI, what is estimate at completion?

$867391.3

$990000

$1196547.62

$1040476.19

#108. For crest vertical curve design with grade change A=3.0%, choose K=48.67 from SSD criteria (given). What curve length L=KA is required?

146 ft

219 ft

16.2 ft

73 ft

#109. During flood routing, why is reservoir stage-storage-discharge relationship essential?

It is only needed for structural concrete mix design

It replaces all need for watershed runoff estimation

It directly gives groundwater recharge without mass balance

It links inflow hydrograph to time-varying outflow and storage for routing computations

#110. Using Greenshields model v=vf(1-k/kj), maximum flow occurs at k=kj/2. For vf=55 mph and kj=140 veh/mi/ln, what is qmax?

70 veh/h/ln

962.5 veh/h/ln

1925 veh/h/ln

7700 veh/h/ln

Exam Simulation No. 10

Results

#1. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=320 in^4, span L=312 in. Compute midspan deflection δ=PL^3/(48EI).

#2. Using Greenshields model v=vf(1-k/kj), maximum flow occurs at k=kj/2. For vf=55 mph and kj=180 veh/mi/ln, what is qmax?

#3. A fully restrained steel member has E=204 GPa, α=1.1e-05 /°C, and temperature rise ΔT=105°C. What thermal stress develops (σ=EαΔT)?

#4. A concrete design uses water=204 kg/m^3, w/c=0.4, and cement specific gravity=3.2. What is the absolute volume of cement in 1 m^3 of concrete?

#5. Given specific gravity Gs=2.75, water content w=20%, and void ratio e=0.7, compute degree of saturation Sr=wGs/e.

#6. For earthwork, cross-sectional areas are A1=2113, Am=1278, A2=2527 ft^2 over spacing L=177 ft. What volume by prismoidal formula?

#7. For a reinforced concrete beam, As=4.0 in^2, fy=75 ksi, d=20 in, a=2.5 in. Compute design moment φMn with Mn=Asfy(d-a/2), φ=0.9.

#8. Which method is commonly used to solve elementary statically indeterminate beams by compatibility and superposition?

#9. A rehabilitation program costs $13000 at year-end for 5 years. At interest rate 6%, what is the present worth?

#10. A plane truss has m=23 members, j=16 joints, r=5 reaction components. What is degree of static indeterminacy m+r-2j?

#11. A particle starts with speed 8 ft/s and constant acceleration 2 ft/s^2 over displacement 168 ft. Using v^2=v0^2+2as, what is final speed?

#12. A rehabilitation program costs $23000 at year-end for 7 years. At interest rate 9%, what is the present worth?

#13. CPM network has two parallel paths from start to finish: Path 1 durations 6 and 6 days; Path 2 durations 4 and 6 days. What is project duration?

#14. Two retaining-wall faces are modeled by parallel lines 5x + 4y + (-14) = 0 and 5x + 4y + 13 = 0, with coordinates in ft. What is the perpendicular separation between the faces?

#15. A concrete design uses water=163 kg/m^3, w/c=0.5, and cement specific gravity=3.1. What is the absolute volume of cement in 1 m^3 of concrete?

#16. At status date: BAC=$1,200,000, EV=$420,000, AC=$610,000. Assume future cost performance follows current CPI. Using EAC=BAC/CPI, what is estimate at completion?

#17. Coordinates of a triangular lot are (1261,2910), (1688,2910), (1360,3099) ft. What is the area by coordinate method?

#18. A signalized intersection has heavy left-turn demand causing spillback. Which control strategy is most direct for reducing opposing-flow conflicts and delay?

#19. In Hardy Cross analysis of looped distribution systems, what condition must be satisfied at convergence for each loop?

#20. An asphalt overlay covers 560 m × 22 m at compacted thickness 0.25 m. Use mix density 2500 kg/m^3 and supply+place cost $95/metric ton. What is estimated cost?

#21. For stress state σx=111 MPa, σy=-16 MPa, τxy=36 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

#22. A detention pond outlet is redesigned to reduce post-development peak flow to pre-development levels. Which principle is most directly applied?

#23. A flood-mitigation project provides immediate present-value benefits of $338000. Initial cost is $153000 plus annual O&M of $17000 for 9 years at 7%. What is the benefit-cost ratio?

#24. Flow in a reducer has D1=0.5 m, D2=0.15 m, and upstream velocity V1=1.2 m/s. By continuity, what is V2?

#25. A geotechnical alert model flags instability (event B). Prior probability of true instability A is 0.2. Sensitivity P(B|A)=0.7, false-positive rate P(B|not A)=0.1. What is P(A|B)?

#26. Coordinates of a triangular lot are (1778,1295), (2226,1295), (2063,1540) ft. What is the area by coordinate method?

#27. For crest vertical curve design with grade change A=6.0%, choose K=48.67 from SSD criteria (given). What curve length L=KA is required?

#28. A particle starts with speed 24 ft/s and constant acceleration 1 ft/s^2 over displacement 69 ft. Using v^2=v0^2+2as, what is final speed?

#29. A contract has original value $2,420,000 and approved change orders $165,000. Previous paid progress was 45% of current contract value; this month total earned reaches 68%. With 5% retainage on current earnings, what payment is due this month?

#30. A bid has direct costs: labor $180,000, equipment $95,000, materials $330,000, subcontracts $160,000. Apply bond 1.0%, overhead 8%, and fee 10% to direct cost. What is total bid?

#31. A steel member (α=6.5e-06/°F) is 60 ft long and heats by 99°F. What free thermal expansion occurs?

#32. Traverse has two legs: 287 m at azimuth 57°, then 373 m at azimuth 145°. What is straight-line distance from start to end?

#33. Using LRFD combo U=1.2D+1.6L+0.5W with D=61 kip, L=36 kip, W=40 kip, what is factored load U?

#34. A rectangular plate 7m×8m has a centered rectangular hole 5m×5m. What is ȳ from the base?

#35. In slope stability analyses, increasing positive pore-water pressure along a potential slip surface generally causes what effect?

#36. For the circle (x–1)^2 + (y-4)^2 = 81 and the line y = -0.5x + 12.67, how many real intersection points are there?

#37. For a rectangle b=12 in, h=12 in, find I_x about an axis parallel to centroidal x-axis and offset by d=4 in using parallel-axis theorem.

#38. Using NRCS runoff method: for storm P=3.0 in and curve number CN=85, compute runoff depth Q (in).

#39. A circular shaft transmits torque T=5000 N·mm. At radius r=33 mm with polar moment J=200000 mm^4, what is torsional shear stress τ=Tr/J?

#40. A concrete design uses water=161 kg/m^3, w/c=0.45, and cement specific gravity=3.2. What is the absolute volume of cement in 1 m^3 of concrete?

#41. Flow in a reducer has D1=0.4 m, D2=0.15 m, and upstream velocity V1=1.2 m/s. By continuity, what is V2?

#42. In the four-step travel demand model, where are origin-destination movements between zones estimated?

#43. Lime stabilization of clayey subgrade is primarily used to achieve which combined effect?

#44. A sediment basin excavation covers 6.2 acres to average depth 2.0 ft. A dozer spread has nominal output 900 yd^3/day with site efficiency 0.75. How many full days are required (ignore weather)?

#45. For stress state σx=61 MPa, σy=-43 MPa, τxy=39 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

#46. In Hardy Cross analysis of looped distribution systems, what condition must be satisfied at convergence for each loop?

#47. A unit-price contract has a bid item quantity underrun. Original amount is $74200. A signed change order adds $6100 for additional dewatering. What is the revised contract amount?

#48. A simply supported beam span 16 ft has full-span UDL w=6 kip/ft plus point load P=12 kip at x=11 ft from left. What is the maximum positive bending moment (approx., governing critical section)?

#49. A 21 kg cart increases speed from 5 m/s to 14 m/s on level track. Neglecting losses, what net work is required?

#50. For c=0 strip footing approximation qult=γDfNq+0.5γBNγ. Given γ=17, Df=2.0 m, B=1.5 m, Nq=22, Nγ=20, find qult.

#51. Direct shear test interpretation gives c=18 kPa and φ=28°. At normal stress 80 kPa, what peak shear stress is predicted?

#52. A plane truss has m=30 members, j=18 joints, r=3 reaction components. What is degree of static indeterminacy m+r-2j?

#53. An asphalt overlay covers 420 m × 26 m at compacted thickness 0.3 m. Use mix density 2400 kg/m^3 and supply+place cost $125/metric ton. What is estimated cost?

#54. Two coplanar forces act at a point: F1 = 14 lb at 54° from +x and F2 = 10 lb at 138° from +x. What is resultant magnitude?

#55. A steel tension member has gross area Ag=10.0 in^2 and Fy=65 ksi. If yielding controls with φ=0.9, what is design strength φPn?

#56. Lime stabilization of clayey subgrade is primarily used to achieve which combined effect?

#57. A triangular construction lot has vertices at (0,0), (14,3), and (4,13) in a Cartesian site grid measured in m. Using the shoelace method, what is the lot area?

#58. Between two points in water system: p1=180 kPa, z1=102.0 m, V1=1.2 m/s; p2=80 kPa, z2=100.0 m, V2=2.0 m/s; headloss=2.5 m. Required pump head?

#59. Simply supported beam L=36 ft has UDL w=1.2 kip/ft plus point load P=10 kip at a=12 ft from left. What is governing positive moment (critical section approximation)?

#60. A force with components Fx = -19 lb, Fy = 17 lb is applied at position (x, y)=(8, 2) ft from O. What is scalar moment M_O = xFy – yFx?

#61. A consultant deviates from accepted pavement testing standards and the owner incurs $297000 in corrective work. Which legal theory most directly supports owner recovery?

#62. Direct shear test interpretation gives c=8 kPa and φ=28°. At normal stress 80 kPa, what peak shear stress is predicted?

#63. Lines 3x + 1y = -15 and 2x + (-4)y = 12 intersect at P. What is the equation of the line through P that is perpendicular to y = 3x + 1?

#64. Two coplanar forces act at a point: F1 = 20 N at 50° from +x and F2 = 15 N at 129° from +x. What is resultant magnitude?

#65. A slender rod of mass 9 kg and length 6 m rotates about its centroidal axis perpendicular to the rod. What is mass moment of inertia?

#66. A unit-price contract has a bid item quantity underrun. Original amount is $71800. A signed change order adds $6200 for additional dewatering. What is the revised contract amount?

#67. A project has three mutually exclusive outcomes: high gain $218000 with probability 30%, moderate gain $124000 with probability 10%, and loss $127000 otherwise. What is expected value?

#68. A unit-price contract has a bid item quantity underrun. Original amount is $57000. A signed change order adds $10000 for additional dewatering. What is the revised contract amount?

#69. For stress state σx=164 MPa, σy=-34 MPa, τxy=87 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

#70. A signalized intersection has heavy left-turn demand causing spillback. Which control strategy is most direct for reducing opposing-flow conflicts and delay?

#71. Using NRCS runoff method: for storm P=3.5 in and curve number CN=75, compute runoff depth Q (in).

#72. Differential leveling run: BM elev=242 ft; BS1=6.37 ft, FS1=4.83 ft, BS2=3.02 ft, FS2=4.83 ft. What is ending elevation?

#73. A fine-grained soil plots above the A-line with LL=62 and PI=34. Under USCS, what classification is most likely?

#74. A flood-mitigation project provides immediate present-value benefits of $360000. Initial cost is $340000 plus annual O&M of $12000 for 8 years at 6%. What is the benefit-cost ratio?

#75. Material test results occur at values 13, 35, and 47 MPa with frequencies 7, 10, and 6. What is the weighted mean strength?

#76. Coordinates of a triangular lot are (1633,1719), (1972,1719), (1749,1926) ft. What is the area by coordinate method?

#77. Between two points in water system: p1=220 kPa, z1=110.0 m, V1=1.8 m/s; p2=60 kPa, z2=95.0 m, V2=2.0 m/s; headloss=3.5 m. Required pump head?

#78. Flow in a reducer has D1=0.4 m, D2=0.25 m, and upstream velocity V1=1.8 m/s. By continuity, what is V2?