FE CIVIL – THIRD SIMULATION

#1. Given specific gravity Gs=2.65, water content w=12%, and void ratio e=0.7, compute degree of saturation Sr=wGs/e.

54.57%

4.54%

45.43%

30.94%

#2. A circular sewer flows full with D=0.3 m, slope S=0.0025, Manning n=0.015. Estimate capacity Q using Manning equation.

0.0419 m^3/s

0.0629 m^3/s

0.0002 m^3/s

0.021 m^3/s

#3. A circular shaft transmits torque T=2000 N·mm. At radius r=40 mm with polar moment J=1000000 mm^4, what is torsional shear stress τ=Tr/J?

0.08 MPa

12.5 MPa

0.0001 MPa

3.2 MPa

#4. A rehabilitation program costs $24000 at year-end for 5 years. At interest rate 8%, what is the present worth?

$110198.8

$300000

$95825.04

$120000

#5. For earthwork, cross-sectional areas are A1=1449, Am=1734, A2=1923 ft^2 over spacing L=141 ft. What volume by prismoidal formula?

242238 ft^3

8971.778 ft^3

237726 ft^3

239982 ft^3

#6. Two coplanar forces act at a point: F1 = 10 N at 43° from +x and F2 = 24 N at 101° from +x. What is resultant magnitude?

30.5 N

14 N

34 N

36.6 N

#7. 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

#8. A project requires transforming GNSS latitude/longitude points into local design coordinates tied to a state plane grid. Which sequence is most appropriate?

Apply datum-consistent geodetic-to-grid projection, then local site calibration if specified

Use only orthometric heights to derive plan coordinates

Convert directly to magnetic bearings and ignore projection

Use arbitrary scaling of lat/long differences as feet

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

It directly gives groundwater recharge without mass balance

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

It replaces all need for watershed runoff estimation

It is only needed for structural concrete mix design

#10. A particle starts with speed 13 m/s and constant acceleration 6 m/s^2 over displacement 180 m. Using v^2=v0^2+2as, what is final speed?

1093 m/s

0 m/s

48.26 m/s

2329 m/s

#11. For a retaining wall with uniform surcharge q=10 kPa and active coefficient Ka=0.28, what is lateral force from surcharge over height H=7 m (per meter length)?

9.8 kN/m

39.2 kN/m

19.6 kN/m

2.8 kN/m

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

Reduce plasticity and swell potential while improving strength/workability

Increase organic content for compressibility

Eliminate need for moisture-density control

Create fully impermeable layer regardless compaction

#13. A steel member (α=6.0e-06/°F) is 25 ft long and heats by 107°F. What free thermal expansion occurs?

0.1926 ft

0.0013 ft

0.0006 ft

0.0161 ft

#14. A fully restrained steel member has E=199 GPa, α=1.2e-05 /°C, and temperature rise ΔT=89°C. What thermal stress develops (σ=EαΔT)?

2.39 MPa (compression)

212.53 MPa (compression)

2125.32 MPa (compression)

4.27 MPa

#15. A force with components Fx = -3 lb, Fy = -13 lb is applied at position (x, y)=(4, 3) ft from O. What is scalar moment M_O = xFy – yFx?

-112 lb-ft

-61 lb-ft

-43 lb-ft

43 lb-ft

#16. Two direction vectors are u=[6, -1, 2] and v=[6, 2, 6]. What is the angle between them in degrees?

46 deg

145.49 deg

34.51 deg

55.49 deg

#17. A floor framing plan shows beam B3 at grid intersection C-5, while a general note states all beam marks reference the beam schedule for size, camber, and connection type. Which workflow best ensures correct field installation?

Install any W-shape with similar depth because location governs only

Use column schedule for beam camber and skip connection details

Follow only architectural reflected ceiling plan for steel member size

Locate B3 on plan, then use beam schedule and referenced connection details before fabrication

#18. 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?

5.53 m

-1.97 m

-0.53 m

0.53 m

#19. Three edge vectors of a skewed material cell are a=[0, 3, -3], b=[0, -1, 0], c=[1, 1, 4] (ft). What is the cell volume |a·(b×c)|?

3 ft^3

6 ft^3

1.5 ft^3

5 ft^3

#20. A project allocates overhead to all departments, but one alternative requires dedicated temporary traffic control staff not used otherwise. How should this staff cost be treated in alternative selection?

As a non-economic externality excluded from analysis

As an incremental direct cost attributable to that alternative

As a sunk cost because payroll exists

As an unavoidable fixed cost identical for all alternatives

#21. A mat foundation is often selected over isolated spread footings when:

Only temporary structures are supported

Column loads are heavy and individual footing areas would occupy most of the building footprint

Bedrock is shallow and loads are very light

Differential settlement is irrelevant

#22. Using NRCS runoff method: for storm P=3.5 in and curve number CN=85, compute runoff depth Q (in).

2.823 in

0.598 in

2.016 in

1.484 in

#23. A sediment basin excavation covers 8.0 acres to average depth 1.0 ft. A dozer spread has nominal output 1500 yd^3/day with site efficiency 0.85. How many full days are required (ignore weather)?

11 days

9 days

13 days

8.6 days

#24. A PE licensed in one jurisdiction receives a temporary permit in another for emergency flood response. After 24 hours, the PE continues design work outside the temporary permit scope. What is the best compliance interpretation?

Temporary permits eliminate all board oversight requirements

The PE must stop out-of-scope practice and obtain proper authorization before continuing

Any PE license allows unrestricted permanent practice in all jurisdictions

Scope limits apply only to structural projects, not civil work

#25. A rehabilitation program costs $25000 at year-end for 10 years. At interest rate 8%, what is the present worth?

$167752.03

$250000

$192914.84

$312500

#26. A rectangular plate 9m×12m has a centered rectangular hole 4m×3m. What is ȳ from the base?

5.55 m

6.56 m

4.5 m

6 m

#27. A plane truss has m=30 members, j=17 joints, r=4 reaction components. What is degree of static indeterminacy m+r-2j?

0

1

2

3

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

Trip generation only

Mode choice calibration only

Traffic assignment only

Trip distribution step

#29. Between two points in water system: p1=220 kPa, z1=110.0 m, V1=1.2 m/s; p2=60 kPa, z2=100.0 m, V2=2.0 m/s; headloss=3.0 m. Required pump head?

-2.03 m

-10.03 m

-7.03 m

7.03 m

#30. A block of weight 293 lb is on a 15° incline with μs=0.45. What minimum force parallel to plane is required to start moving it up the incline?

283.02 lb

203.19 lb

131.85 lb

-51.52 lb

#31. Below groundwater table at depth z=4.0 m, with γsat=20.0 kN/m^3, what vertical effective stress increment develops?

39.24 kPa

80 kPa

20.38 kPa

40.76 kPa

#32. Below groundwater table at depth z=4.0 m, with γsat=20.5 kN/m^3, what vertical effective stress increment develops?

21.38 kPa

42.76 kPa

39.24 kPa

82 kPa

#33. 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

292 ft

438 ft

8.1 ft

#34. A mat foundation is often selected over isolated spread footings when:

Differential settlement is irrelevant

Only temporary structures are supported

Bedrock is shallow and loads are very light

Column loads are heavy and individual footing areas would occupy most of the building footprint

#35. Same steel column has K=0.7 for frame A and K=1.2 for frame B. What is ratio Pcr,A / Pcr,B?

0.583

0.34

2.939

1.714

#36. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=240 in^4, span L=216 in. Compute midspan deflection δ=PL^3/(48EI).

0.724 in

2.1719 in

0.2413 in

0.0007 in

#37. For crest vertical curve design with grade change A=4.0%, choose K=59 from SSD criteria (given). What curve length L=KA is required?

354 ft

14.8 ft

236 ft

118 ft

#38. 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

Velocity in every pipe segment is the same

All nodal pressures are identical

Algebraic sum of head losses around each closed loop equals zero

#39. 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

#40. A bracing panel is spanned by vectors u=[-4, 7, -2] m and v=[5, -1, -2] m. The panel area equals |u x v|. What is that area?

19.63 m^2

78.51 m^2

39.26 m^2

23 m^2

#41. A pump delivers Q=0.12 m^3/s against total dynamic head H=22 m at efficiency η=0.82. What input power is required?

25.9 kW

31.58 kW

41.06 kW

3.22 kW

#42. Two direction vectors are u=[7, 1, 1] and v=[5, -3, 4]. What is the angle between them in degrees?

44.53 deg

135.47 deg

45.47 deg

36 deg

#43. A vertical rectangular gate (width 3.0 m) retains water to depth 1.8 m. What is resultant hydrostatic force on the gate?

52.97 kN

66.75 kN

47.68 kN

23.84 kN

#44. In a consolidated undrained triaxial test with pore-pressure measurements, what key advantage exists over unconfined compression?

It cannot evaluate undrained response

It allows effective-stress strength parameter interpretation with confining pressure control

It is restricted to clean sands only

It provides only index properties like LL and PL

#45. A steel coupon tested to ASTM tension standards shows yield at 52 ksi and ultimate at 67 ksi. Which interpretation is most accurate for structural design checks?

Only elongation controls member nominal strength

Ultimate strength replaces all need for yield checks in ASD/LRFD

Yield and ultimate are always identical for structural steels

Yield strength primarily governs service-level inelastic onset, while ultimate indicates maximum tensile capacity

#46. Using AASHTO-style SN=a1D1+a2m2D2+a3m3D3, with SN=4.0, a1=0.44, D1=5.0 in, a2=0.14, m2=1.1, and ignoring D3, what base thickness D2 is needed?

16.36 in

28.57 in

7.01 in

11.69 in

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

Method of joints only

Rankine earth-pressure method

Force method (consistent deformations)

Direct stiffness prohibited for indeterminate systems

#48. A project has three mutually exclusive outcomes: high gain $259000 with probability 30%, moderate gain $108000 with probability 10%, and loss $120000 otherwise. What is expected value?

$160500

$16500

$139000

$11550

#49. A simply supported beam span 14 ft carries a uniform load w=6 kip/ft over full span and a point load P=7 kip at 6 ft from A. Find reaction at B.

3 kip

45.5 kip

45 kip

46 kip

#50. A simply supported beam span 11 m has full-span UDL w=12 kN/m plus point load P=16 kN at x=7 m from left. What is the maximum positive bending moment (approx., governing critical section)?

225.5 kN-m

214.91 kN-m

838 kN-m

203.5 kN-m

#51. Two coplanar forces act at a point: F1 = 11 N at 69° from +x and F2 = 11 N at 156° from +x. What is resultant magnitude?

0 N

22 N

19.15 N

15.96 N

#52. A bid has direct costs: labor $300,000, equipment $95,000, materials $330,000, subcontracts $120,000. Apply bond 1.5%, overhead 8%, and fee 10% to direct cost. What is total bid?

$997100

$1022450

$1009775

$845000

#53. In a consolidated undrained triaxial test with pore-pressure measurements, what key advantage exists over unconfined compression?

It allows effective-stress strength parameter interpretation with confining pressure control

It is restricted to clean sands only

It cannot evaluate undrained response

It provides only index properties like LL and PL

#54. Same steel column has K=1.0 for frame A and K=1.0 for frame B. What is ratio Pcr,A / Pcr,B?

0.72

1

1.16

0.84

#55. A horizontal curve is represented by x^2 + y^2 + (-4)x + (8)y + (-61) = 0. What is the radius of the circle?

81

6

4.47

9

#56. A grading detail indicates slope 1V:8H. If vertical rise is 1.5 m, what horizontal run is required?

0.188 m

5.33 m

12 m

6 m

#57. For stress state σx=159 MPa, σy=52 MPa, τxy=30 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

61.34 MPa

105.5 MPa

107 MPa

53.5 MPa

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

-2

5

4

-4

#59. A grading detail indicates slope 1V:8H. If vertical rise is 1.0 m, what horizontal run is required?

9.28 m

4 m

0.125 m

8 m

#60. A dimensionless loading index is modeled by f(x) = 2x^2 + 3/x for x in [3, 7]. Compute I = integral from 3 to 7 of f(x) dx.

216.21

106.6

222.67

213.21

#61. Using AASHTO-style SN=a1D1+a2m2D2+a3m3D3, with SN=3.2, a1=0.44, D1=6.0 in, a2=0.14, m2=0.9, and ignoring D3, what base thickness D2 is needed?

2.67 in

4.44 in

22.86 in

6.22 in

#62. A sediment basin excavation covers 6.2 acres to average depth 1.5 ft. A dozer spread has nominal output 1200 yd^3/day with site efficiency 0.75. How many full days are required (ignore weather)?

19 days

17 days

12.5 days

15 days

#63. A block of weight 277 N is on a 15° incline with μs=0.3. What minimum force parallel to plane is required to start moving it up the incline?

151.96 N

267.56 N

83.1 N

-8.58 N

#64. For an asphalt mix with binder content 5.2% by total mass, Gsb=2.7, and bulk mix specific gravity Gmb=2.35, estimate air voids Va (%).

89.98%

7.01%

13.02%

10.02%

#65. A PE licensed in one jurisdiction receives a temporary permit in another for emergency flood response. After 24 hours, the PE continues design work outside the temporary permit scope. What is the best compliance interpretation?

The PE must stop out-of-scope practice and obtain proper authorization before continuing

Temporary permits eliminate all board oversight requirements

Any PE license allows unrestricted permanent practice in all jurisdictions

Scope limits apply only to structural projects, not civil work

#66. Flow in a reducer has D1=0.5 m, D2=0.2 m, and upstream velocity V1=1.5 m/s. By continuity, what is V2?

14.062 m/s

9.375 m/s

4.688 m/s

0.24 m/s

#67. Using LRFD combo U=1.2D+1.6L+0.5W with D=79 kip, L=80 kip, W=67 kip, what is factored load U?

236.3 kip

226 kip

246.6 kip

256.3 kip

#68. Estimate concrete paving cost for area 31500 ft^2, thickness 8 in, waste 10%, and installed unit cost $165/yd^3. What is estimated item cost?

$141166.67

$128333.33

$169400

$163753.3372

#69. For earthwork, cross-sectional areas are A1=1535, Am=1903, A2=1438 ft^2 over spacing L=63 ft. What volume by prismoidal formula?

4116.389 ft^3

93649.5 ft^3

102396 ft^3

111142.5 ft^3

#70. A concrete acceptance plan uses compressive tests at 7 and 28 days. Why are both ages useful?

Only 7-day values matter because hydration stops after one week

28-day values are ignored if slump is within limits

7-day strength tracks early gain and curing quality; 28-day strength is the primary specification basis

Both are used only to compute modulus of rupture directly

#71. A simply supported beam with centered load P=12 kip has E=29000 ksi, I=180 in^4, span L=264 in. Compute midspan deflection δ=PL^3/(48EI).

0.0006 in

2.6436 in

0.8812 in

0.2937 in

#72. Differential leveling run: BM elev=500 ft; BS1=4.83 ft, FS1=6.69 ft, BS2=4.84 ft, FS2=3.03 ft. What is ending elevation?

519.39 ft

504.94 ft

500.06 ft

499.94 ft

#73. 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).

0.0009 in

3.9655 in

1.3218 in

0.4406 in

#74. A particle starts with speed 9 ft/s and constant acceleration 6 ft/s^2 over displacement 187 ft. Using v^2=v0^2+2as, what is final speed?

1131 ft/s

0 ft/s

48.22 ft/s

2325 ft/s

#75. A project has three mutually exclusive outcomes: high gain $204000 with probability 20%, moderate gain $151000 with probability 15%, and loss $130000 otherwise. What is expected value?

$74000

$147950

$-21050

$-14735

#76. For a rectangle b=12 in, h=16 in, find I_x about an axis parallel to centroidal x-axis and offset by d=2 in using parallel-axis theorem.

4096 in^4

4864 in^4

4100 in^4

768 in^4

#77. Flow in a reducer has D1=0.4 m, D2=0.25 m, and upstream velocity V1=1.5 m/s. By continuity, what is V2?

0.586 m/s

3.84 m/s

5.76 m/s

1.92 m/s

#78. A project requires transforming GNSS latitude/longitude points into local design coordinates tied to a state plane grid. Which sequence is most appropriate?

Apply datum-consistent geodetic-to-grid projection, then local site calibration if specified

Convert directly to magnetic bearings and ignore projection

Use only orthometric heights to derive plan coordinates

Use arbitrary scaling of lat/long differences as feet

#79. A 32 kg block slides down a 15° incline with kinetic friction μ=0.15. What is acceleration magnitude along plane (g=9.81 m/s^2)?

2.54 m/s^2

1.47 m/s^2

1.12 m/s^2

3.96 m/s^2

#80. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=320 in^4, span L=216 in. Compute midspan deflection δ=PL^3/(48EI).

0.181 in

0.0006 in

1.6289 in

0.543 in

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

Increase posted speed through intersection

Use stop control on all approaches simultaneously

Provide protected left-turn phasing with optimized cycle split

Remove all left-turn lanes

#82. 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?

650 kip

491.4 kip

702 kip

585 kip

#83. A flood-mitigation project provides immediate present-value benefits of $330000. Initial cost is $248000 plus annual O&M of $14000 for 11 years at 6%. What is the benefit-cost ratio?

0.921

-0.079

1.086

1.271

#84. A simply supported beam span 8 m has full-span UDL w=4 kN/m plus point load P=6 kN at x=5 m from left. What is the maximum positive bending moment (approx., governing critical section)?

38 kN-m

158 kN-m

41.63 kN-m

44 kN-m

#85. A geotechnical alert model flags instability (event B). Prior probability of true instability A is 0.35. Sensitivity P(B|A)=0.8, false-positive rate P(B|not A)=0.1. What is P(A|B)?

0.345

0.8116

0.1884

0.7

#86. For a confined aquifer drawdown screening (Cooper-Jacob style), with pumping Q=700 m^3/day, transmissivity T=650 m^2/day, and dimensionless log term log10(…)=2.903, estimate drawdown coefficient part s=Q/(2πT)*log term.

0.498 m

1.077 m

0.249 m

0.995 m

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

Increase posted speed through intersection

Use stop control on all approaches simultaneously

Remove all left-turn lanes

Provide protected left-turn phasing with optimized cycle split

#88. Engineer Jordan is asked to certify a retaining wall design prepared by another firm without reviewing calculations. The owner says schedule pressure requires immediate certification. Under professional ethics, what is the most defensible action?

Decline certification until competent review verifies the design meets standards

Certify if the original firm verbally confirms accuracy

Certify immediately because the owner accepts all risk

Stamp only the title sheet to avoid full responsibility

#89. A steel member (α=6.5e-06/°F) is 71 ft long and heats by 77°F. What free thermal expansion occurs?

0.4264 ft

0.003 ft

0.0005 ft

0.0355 ft

#90. A force with components Fx = -12 lb, Fy = -5 lb is applied at position (x, y)=(5, 4) ft from O. What is scalar moment M_O = xFy – yFx?

-73 lb-ft

23 lb-ft

26.45 lb-ft

-153 lb-ft

#91. A 42 kg cart increases speed from 3 m/s to 13 m/s on level track. Neglecting losses, what net work is required?

2100 J

420 J

-3360 J

3360 J

#92. A public owner wants early constructor input during design, guaranteed maximum price later, and single-point coordination of trade packages before 100% design completion. Which delivery approach best fits?

Bridging only with no preconstruction services

Pure design-bid-build with lump-sum bid after full design

Construction Manager at Risk (CMAR)

Unit-price contract with no schedule responsibility

#93. A rehabilitation program costs $23000 at year-end for 10 years. At interest rate 9%, what is the present worth?

$169747.05

$255555.56

$147606.13

$230000

#94. Water at 20°C has ν=1.0e-06 m^2/s in a pipe with V=2.0 m/s and D=0.1 m. What Reynolds number Re=VD/ν?

20000

20000000

2000000

200000

#95. Two direction vectors are u=[5, 1, 5] and v=[7, -2, 7]. What is the angle between them in degrees?

68 deg

19.47 deg

160.53 deg

70.53 deg

#96. Assume X is normally distributed with mean 36 and standard deviation 10. What is P(21 <= X <= 51)?

0.8664

0.4332

0.9332

0.1336

#97. Water at 20°C has ν=1.0e-06 m^2/s in a pipe with V=0.8 m/s and D=0.1 m. What Reynolds number Re=VD/ν?

80000

8000000

8000

800000

#98. A circular shaft transmits torque T=10000 N·mm. At radius r=20 mm with polar moment J=900000 mm^4, what is torsional shear stress τ=Tr/J?

0.2222 MPa

4.4444 MPa

0.0006 MPa

4.5 MPa

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

Direct stiffness prohibited for indeterminate systems

Force method (consistent deformations)

Method of joints only

Rankine earth-pressure method

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

Traffic assignment only

Mode choice calibration only

Trip distribution step

Trip generation only

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

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

It replaces all need for watershed runoff estimation

It is only needed for structural concrete mix design

It directly gives groundwater recharge without mass balance

#102. Coordinates of a triangular lot are (1929,1696), (2078,1696), (2035,1933) ft. What is the area by coordinate method?

8828.25 ft^2

17656.5 ft^2

132.88 ft^2

35313 ft^2

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

Reduce plasticity and swell potential while improving strength/workability

Eliminate need for moisture-density control

Increase organic content for compressibility

Create fully impermeable layer regardless compaction

#104. A circular sewer flows full with D=0.6 m, slope S=0.0025, Manning n=0.013. Estimate capacity Q using Manning equation.

0.0007 m^3/s

0.4605 m^3/s

0.1535 m^3/s

0.307 m^3/s

#105. A PE licensed in one jurisdiction receives a temporary permit in another for emergency flood response. After 24 hours, the PE continues design work outside the temporary permit scope. What is the best compliance interpretation?

Any PE license allows unrestricted permanent practice in all jurisdictions

Temporary permits eliminate all board oversight requirements

Scope limits apply only to structural projects, not civil work

The PE must stop out-of-scope practice and obtain proper authorization before continuing

#106. A vertical rectangular gate (width 2.0 m) retains water to depth 1.8 m. What is resultant hydrostatic force on the gate?

44.5 kN

35.32 kN

15.89 kN

31.78 kN

#107. A simply supported beam span 20 m has full-span UDL w=12 kN/m plus point load P=19 kN at x=15 m from left. What is the maximum positive bending moment (approx., governing critical section)?

647.5 kN-m

648.44 kN-m

695 kN-m

2685 kN-m

#108. A contract has original value $1,250,000 and approved change orders $165,000. Previous paid progress was 35% of current contract value; this month total earned reaches 62%. With 8% retainage on current earnings, what payment is due this month?

$382050

$351486

$807116

$449902.08

#109. A circular shaft transmits torque T=10000 N·mm. At radius r=13 mm with polar moment J=200000 mm^4, what is torsional shear stress τ=Tr/J?

0.65 MPa

1.5385 MPa

8.45 MPa

0.0038 MPa

Exam Simulation No. 3

Results

#1. Given specific gravity Gs=2.65, water content w=12%, and void ratio e=0.7, compute degree of saturation Sr=wGs/e.

#2. A circular sewer flows full with D=0.3 m, slope S=0.0025, Manning n=0.015. Estimate capacity Q using Manning equation.

#3. A circular shaft transmits torque T=2000 N·mm. At radius r=40 mm with polar moment J=1000000 mm^4, what is torsional shear stress τ=Tr/J?

#4. A rehabilitation program costs $24000 at year-end for 5 years. At interest rate 8%, what is the present worth?

#5. For earthwork, cross-sectional areas are A1=1449, Am=1734, A2=1923 ft^2 over spacing L=141 ft. What volume by prismoidal formula?

#6. Two coplanar forces act at a point: F1 = 10 N at 43° from +x and F2 = 24 N at 101° from +x. What is resultant magnitude?

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

#8. A project requires transforming GNSS latitude/longitude points into local design coordinates tied to a state plane grid. Which sequence is most appropriate?

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

#10. A particle starts with speed 13 m/s and constant acceleration 6 m/s^2 over displacement 180 m. Using v^2=v0^2+2as, what is final speed?

#11. For a retaining wall with uniform surcharge q=10 kPa and active coefficient Ka=0.28, what is lateral force from surcharge over height H=7 m (per meter length)?

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

#13. A steel member (α=6.0e-06/°F) is 25 ft long and heats by 107°F. What free thermal expansion occurs?

#14. A fully restrained steel member has E=199 GPa, α=1.2e-05 /°C, and temperature rise ΔT=89°C. What thermal stress develops (σ=EαΔT)?

#15. A force with components Fx = -3 lb, Fy = -13 lb is applied at position (x, y)=(4, 3) ft from O. What is scalar moment M_O = xFy – yFx?

#16. Two direction vectors are u=[6, -1, 2] and v=[6, 2, 6]. What is the angle between them in degrees?

#17. A floor framing plan shows beam B3 at grid intersection C-5, while a general note states all beam marks reference the beam schedule for size, camber, and connection type. Which workflow best ensures correct field installation?

#18. 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?

#19. Three edge vectors of a skewed material cell are a=[0, 3, -3], b=[0, -1, 0], c=[1, 1, 4] (ft). What is the cell volume |a·(b×c)|?

#20. A project allocates overhead to all departments, but one alternative requires dedicated temporary traffic control staff not used otherwise. How should this staff cost be treated in alternative selection?

#21. A mat foundation is often selected over isolated spread footings when:

#22. Using NRCS runoff method: for storm P=3.5 in and curve number CN=85, compute runoff depth Q (in).

#23. A sediment basin excavation covers 8.0 acres to average depth 1.0 ft. A dozer spread has nominal output 1500 yd^3/day with site efficiency 0.85. How many full days are required (ignore weather)?

#24. A PE licensed in one jurisdiction receives a temporary permit in another for emergency flood response. After 24 hours, the PE continues design work outside the temporary permit scope. What is the best compliance interpretation?

#25. A rehabilitation program costs $25000 at year-end for 10 years. At interest rate 8%, what is the present worth?

#26. A rectangular plate 9m×12m has a centered rectangular hole 4m×3m. What is ȳ from the base?

#27. A plane truss has m=30 members, j=17 joints, r=4 reaction components. What is degree of static indeterminacy m+r-2j?

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

#29. Between two points in water system: p1=220 kPa, z1=110.0 m, V1=1.2 m/s; p2=60 kPa, z2=100.0 m, V2=2.0 m/s; headloss=3.0 m. Required pump head?

#30. A block of weight 293 lb is on a 15° incline with μs=0.45. What minimum force parallel to plane is required to start moving it up the incline?

#31. Below groundwater table at depth z=4.0 m, with γsat=20.0 kN/m^3, what vertical effective stress increment develops?

#32. Below groundwater table at depth z=4.0 m, with γsat=20.5 kN/m^3, what vertical effective stress increment develops?

#33. 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?

#34. A mat foundation is often selected over isolated spread footings when:

#35. Same steel column has K=0.7 for frame A and K=1.2 for frame B. What is ratio Pcr,A / Pcr,B?

#36. A simply supported beam with centered load P=24 kip has E=29000 ksi, I=240 in^4, span L=216 in. Compute midspan deflection δ=PL^3/(48EI).

#37. For crest vertical curve design with grade change A=4.0%, choose K=59 from SSD criteria (given). What curve length L=KA is required?

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

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

#40. A bracing panel is spanned by vectors u=[-4, 7, -2] m and v=[5, -1, -2] m. The panel area equals |u x v|. What is that area?

#41. A pump delivers Q=0.12 m^3/s against total dynamic head H=22 m at efficiency η=0.82. What input power is required?

#42. Two direction vectors are u=[7, 1, 1] and v=[5, -3, 4]. What is the angle between them in degrees?

#43. A vertical rectangular gate (width 3.0 m) retains water to depth 1.8 m. What is resultant hydrostatic force on the gate?

#44. In a consolidated undrained triaxial test with pore-pressure measurements, what key advantage exists over unconfined compression?

#45. A steel coupon tested to ASTM tension standards shows yield at 52 ksi and ultimate at 67 ksi. Which interpretation is most accurate for structural design checks?

#46. Using AASHTO-style SN=a1D1+a2m2D2+a3m3D3, with SN=4.0, a1=0.44, D1=5.0 in, a2=0.14, m2=1.1, and ignoring D3, what base thickness D2 is needed?

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

#48. A project has three mutually exclusive outcomes: high gain $259000 with probability 30%, moderate gain $108000 with probability 10%, and loss $120000 otherwise. What is expected value?

#49. A simply supported beam span 14 ft carries a uniform load w=6 kip/ft over full span and a point load P=7 kip at 6 ft from A. Find reaction at B.

#50. A simply supported beam span 11 m has full-span UDL w=12 kN/m plus point load P=16 kN at x=7 m from left. What is the maximum positive bending moment (approx., governing critical section)?

#51. Two coplanar forces act at a point: F1 = 11 N at 69° from +x and F2 = 11 N at 156° from +x. What is resultant magnitude?

#52. A bid has direct costs: labor $300,000, equipment $95,000, materials $330,000, subcontracts $120,000. Apply bond 1.5%, overhead 8%, and fee 10% to direct cost. What is total bid?

#53. In a consolidated undrained triaxial test with pore-pressure measurements, what key advantage exists over unconfined compression?

#54. Same steel column has K=1.0 for frame A and K=1.0 for frame B. What is ratio Pcr,A / Pcr,B?

#55. A horizontal curve is represented by x^2 + y^2 + (-4)x + (8)y + (-61) = 0. What is the radius of the circle?

#56. A grading detail indicates slope 1V:8H. If vertical rise is 1.5 m, what horizontal run is required?

#57. For stress state σx=159 MPa, σy=52 MPa, τxy=30 MPa, what is in-plane maximum shear stress τmax (Mohr’s circle)?

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

#59. A grading detail indicates slope 1V:8H. If vertical rise is 1.0 m, what horizontal run is required?

#60. A dimensionless loading index is modeled by f(x) = 2x^2 + 3/x for x in [3, 7]. Compute I = integral from 3 to 7 of f(x) dx.

#61. Using AASHTO-style SN=a1D1+a2m2D2+a3m3D3, with SN=3.2, a1=0.44, D1=6.0 in, a2=0.14, m2=0.9, and ignoring D3, what base thickness D2 is needed?

#62. A sediment basin excavation covers 6.2 acres to average depth 1.5 ft. A dozer spread has nominal output 1200 yd^3/day with site efficiency 0.75. How many full days are required (ignore weather)?

#63. A block of weight 277 N is on a 15° incline with μs=0.3. What minimum force parallel to plane is required to start moving it up the incline?

#64. For an asphalt mix with binder content 5.2% by total mass, Gsb=2.7, and bulk mix specific gravity Gmb=2.35, estimate air voids Va (%).

#65. A PE licensed in one jurisdiction receives a temporary permit in another for emergency flood response. After 24 hours, the PE continues design work outside the temporary permit scope. What is the best compliance interpretation?

#66. Flow in a reducer has D1=0.5 m, D2=0.2 m, and upstream velocity V1=1.5 m/s. By continuity, what is V2?

#67. Using LRFD combo U=1.2D+1.6L+0.5W with D=79 kip, L=80 kip, W=67 kip, what is factored load U?

#68. Estimate concrete paving cost for area 31500 ft^2, thickness 8 in, waste 10%, and installed unit cost $165/yd^3. What is estimated item cost?

#69. For earthwork, cross-sectional areas are A1=1535, Am=1903, A2=1438 ft^2 over spacing L=63 ft. What volume by prismoidal formula?

#70. A concrete acceptance plan uses compressive tests at 7 and 28 days. Why are both ages useful?

#71. A simply supported beam with centered load P=12 kip has E=29000 ksi, I=180 in^4, span L=264 in. Compute midspan deflection δ=PL^3/(48EI).

#72. Differential leveling run: BM elev=500 ft; BS1=4.83 ft, FS1=6.69 ft, BS2=4.84 ft, FS2=3.03 ft. What is ending elevation?

#73. 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).

#74. A particle starts with speed 9 ft/s and constant acceleration 6 ft/s^2 over displacement 187 ft. Using v^2=v0^2+2as, what is final speed?

#75. A project has three mutually exclusive outcomes: high gain $204000 with probability 20%, moderate gain $151000 with probability 15%, and loss $130000 otherwise. What is expected value?

#76. For a rectangle b=12 in, h=16 in, find I_x about an axis parallel to centroidal x-axis and offset by d=2 in using parallel-axis theorem.

#77. Flow in a reducer has D1=0.4 m, D2=0.25 m, and upstream velocity V1=1.5 m/s. By continuity, what is V2?

#78. A project requires transforming GNSS latitude/longitude points into local design coordinates tied to a state plane grid. Which sequence is most appropriate?