# FE Exam Summer 2018

#### Subject: Engineering, Physics, Writing

1) A soil sample has a total mass of 23.3 g, a volume of 12 cm3, an oven-dry mass of 21.2g, and a specific gravity of 2.5 for the solids. The void ratio of this soil sample is most nearly?

A) 0.42

B) 0.53

C) 0.62

D) 0.71

2) Given the phase diagram shown for a saturated soil, what is most nearly the void ratio?

A) 0.25

B) 0.49

C) 1.90

D) 3.00

3) The vertical stress at point A due to 6000Ib point load as shown is about:

A) 32 lb/ft2

B) 64 lb/ft2

C) 96 lb/ft2

D) 128 lb/ft2

4) The base of a 2 m wide continuous footing is 1 m below the round surface. The cohesionless soil under the footing has the following properties γ = 1835 Kg /m3 Nc=9.6 Φ =10 Nq=2.7 C= 0.0 Nγ =1.2 If a factor of safety of three is required, the allowable bearing capacity of the soil under the footing is most nearly

A) 17 kPa

B) 23 kPa

C) 49 kPa

D) 70 kPa

5) Given the slope shown, the factor of safety using the Taylor method is most nearly

A) 0.47

B) 2.1

C) 2.3

D) 2.6

6) The y-coordinate (measured from the top) of the centroid for the T-shaped beam is:

A) 0.08 m

B) 0.16 m

C) 0.30 m

D) 0.38 m

7) Find the Y-coordinate of the centroid for the object shown?

A) 5.61

B) 4.61

C) 3.61

D) 2.61

8) The magnitude of the vertical reaction force at the left support is most nearly

A) 1.3 kN

B) 5.0 kN

C) 13 kN

D) 20 kN

9) The magnitude of the maximum vertical shear in the beam is most nearly

A) 13 kN

B) 14 kN

C) 25 kN

D) 39 kN

10) A 20 ft beam carries a load that decreases linearly form a maximum of 350 Ib/ft at its left support to 0 Ib/ft at the mid span of the beam, the maximum reaction is most nearly

A) 2458 lb

B) 1458 lb

C) 1292 lb

D) 2292 lb

11) The vertical deflection at cantilever end is?

A) 1.33 in

B) 0.66 in

C) 1.0 in

D) 0.33 in

12) The shown truss is

A) Unstable

B) Determinate

C) One degree indeterminate

D) Two degree indeterminate

13) The force in member AH is most nearly

A) 300 lb (Compressive)

B) 600 lb (Tension)

C) 670 lb (Compressive)

D) 370 lb (Tension)

14) A person is driving a car on a road that has a gravel surface. A deer suddenly leaps into the road. The road is on a 10% downgrade, and the car is traveling at 50 mph when the deer appears. The driver’s reaction time is 1.5 sec, and the coefficient of friction on the gravel surface is 0.65. The total distance (ft) required to stop is most nearly:

A) 153

B) 222

C) 242

D) 262

15) A driver with a reaction time of 0.5 sec is driving a car down a 5% grade at 89 km/h when a deer runs into the road 0.04 km in front of the car. The road is dry with a coefficient of friction of ƒ=0.7. The distance the car travels from the moment the deer appears until the car comes to a stop is no less than

A) 0.01 km

B) 0.03 km

C) 0.04 km

D) 0.06 km

16) A design requirements for a section of highway with a 1.5% grade are as follows. Design speed= 80 km/h Coefficient of friction= 0.35 Driver reaction time= 2.0 sec Driver eye height= 1.2 m Object (to be avoided) height= 0.2 m The downhill design braking distance for this highway is most nearly

A) 45 m

B) 75 m

C) 100 m

D) 120 m

17) A freeway lane has a volume of 1,400 vehicles / hr and an average vehicle speed of 45 mph. The time spacing (sec) between vehicles (center to center) is most nearly:

A) 2.6

B) 5.2

C) 15

D) 31

18) A freeway route has a horizontal curve with a PI at sta 11+01.86, an intersection angle, theta, of 12°24’00” right, and a radius of 537 m. The PC station is located at

A) Sta 10 + 44

B) Sta 11 + 60

C) Sta 12 + 84

D) Sta 14 + 08

19) What is the max number of bars no 8 can be used for a circular column of 2ft diameter based on max reinforcement ratio?

A) 10

B) 22

C) 23

D) 25

20) A reinforced concrete beam is subjected to a factored moment M ultimate=648ft-kips. For concrete fc’= 4,000 psi, and for steel fy= 60,000psi. The beam is reinforced with eight #8 bars (8/8)2.54=25 mm in two rows, positioned as shown in the figure below. It may be assumed without verification that =0.90. The minimum adequate overall width b (to the nearest whole inch) for this beam is most nearly:

A) 10

B) 12

C) 13

D) 15

21) The cross section of a reinforced concrete beam with tension reinforcement is shown. Assume that the beam is under-reinforced. fc’ = 3000 lbf/in2 fy = 40.000 lbf/in2 As= 3 in2 In accordance with American Concrete Institute (ACI) strength design, the allowable moment capacity of the beam is most nearly

A) 160 ft-kips

B) 180 ft-kips

C) 200 ft-kips

D) 210 ft-kips

22) If the dead load shear force in the beam is 5 kips and the live load shear force in the beam is 15 kips, then the minimum amount of shear reinforcement needed for a center-to-center stirrup spacing of 12 in based on ACI strength design is most nearly?

A) 0.0010 in2

B) 0.0012 in2

C) 0.180 in2

D) 0.300 in2

23) If the area of reinforcing steel per beam is 6.00 in2, the nominal moment capacity of each beam based on ACI strength design is most nearly?

A) 150 ft-kips

B) 160 ft-kips

C) 590 ft-kips

D) 650 ft-kips

24) The lightest W shape (Fy=36 ksi) can carry a maximum moment of 140,000 ft-Ibf with compression flange braced length of every 6 feet is one of the following?

A) W 21 x 44 Answer

B) W 18 x 46

C) W 12 x 65

D) W 16 x 50

25) In accordance with American Institute of Steel Construction (AISC) allowable stress design (ASD) specifications, the allowable axial compressive stress for design purposes is most nearly

A) 40 MPa

B) 50 MPa

C) 65 MPa

D) 75 MPa

26) The span length and cross section of a reinforced concrete beam are shown. The beam is underreinforced. The concrete and reinforcing steel properties are ƒ’c = 3000 lbf/in2, ƒy = 40,000 lbf/in2, and As = 3 in2. Neglecting beam self-weight and based only on the allowable moment capacity of the beam as determined using American Concrete Institute (ACI) strength design specifications, the maximum allowable live load is most nearly:

A) 20,000 lbf

B) 28,000 lbf

C) 35,000 lbf

D) 50,000 lbf

27) The W21 x 44 steel beam shown in the figure below has its compression flange laterally braced at the one-third points over its full length. Assume Fy = 50 ksi and Cb – 1.0 for the critical segment. The maximum factored load Wu (kips/ft) that the beam can carry for this length is most nearly:

A) 2.187 kips

B) 2.444 kips

C) 3.191 kips

D) 3.548 kips

28) All of the following attributes characterizes a force except?

A) Magnitude

B) Direction

C) Line of Action

D) Center of Rotation

29) What is the length of the vectors A+B+C, the sum of three orthogonal vectors

A) 3.5 m

B) 4.3 m

C) 7.1 m

D) 10 m

30) Determine the magnitude of the moment of the 100 N force about the corner A?

A) 120 N.m

B) 640 N.m

C) 320 N.m

D) 240 N.m

31) In the illustrations shown, all of the structures are statically indeterminate except which of the following?

A) Option (a)

B) Option (b)

C) Option (c)

D) Option (d)

32) Find the tensions T1 and T2, in the ropes shown so that the system is in equilibrum?

A) T1 = 50.0 N and T2 = 50.0 N

B) T1 = 50.0 N and T2 = 70.7 N

C) T1 = 70.7 N and T2 = 50.0 N

D) T1 = 70.7 N and T2 = 70.7 N

33) The velocity (in m/sec) of a falling ball is described by the equation v = 32 + t + 6t2. What is the acceleration at time t = 2 seconds?

A) 9.8 m/s2

B) 25 m/s2

C) 32 m/s2

D) 58 m/s2

34) The location of a particle moving in the x-y plane is given by the parametric equations x = t2 + 4t and y = (1/4)t4 – 60t, where x and y are in meters and t is in seconds. What is the particle’s velocity at t = 4 sec?

A) 8.95 m/s

B) 11.3 m/s

C) 12.6 m/s

D) 16.0 m/s

35) A projectile whose mass is 10 kg is fired directly upward from the ground level with an initial velocity of 1000 m/sec. Neglecting the effects of air resistance, what will be the speed of the projectile when it impacts the ground?

A) 707 m/s

B) 981 m/s

C) 1000 m/s

D) 1414 m/s

36) A 100 kg block is pulled along a smooth, flat surface by an external 500 N force. If the coefficient of friction between the block and the surface is 0.15, what acceleration is experienced by the block due to the external force?

A) 3.23 m/s2

B) 3.80 m/s2

C) 4.33 m/s2

D) 5.00 m/s2

37) A projectile is fired from a canon with an initial velocity of 1000 m/sec and at an angle of 30o from the horizontal. What distance from the canon will the projectile strike the ground if the point of impact is 1500 m below the point of release?

A) 8200 m

B) 67,300 m

C) 78,200 m

D) 90,800 m

38) A constant force of 750 N is applied through a pulley system to lift a mass of 50 kg as shown. Neglecting the mass and friction of the pulley system, what is the acceleration of the 50 kg mass?

A) 5.20 m/s2

B) 8.72 m/s2

C) 16.2 m/s2

D) 20.2 m/s2

39) Traffic travels at 100 km/hr around a banked highway curve with a radius of 1000 m. What banking angle is necessary such that friction will not be required to resist the centrifugal force?

A) 1.40

B) 2.80

C) 4.50

D) 4.60