Civil and Environmental Engineering Answers

The design of a concrete mix requires 1173 kg/m3

of gravel in dry condition, 582 kg/m3

of sand in

dry condition, and 157 kg/m3

of free water. The gravel available at the job site has a moisture

content of 0.8% and absorption of 1.5%, and the available sand has a moisture content of 1.1%

Design the concrete mix according to the following conditions:

Design Environment

 Pavement slab, Bozeman, Montana (cold climate)

 Required design strength = 3,000 psi

 Minimum dimension = 12 in

 Statistical data indicate a standard deviation of compressive strength of 250 psi is expected

(more than 30 samples).

 Only air entrainer is allowed.

Available Materials

 Air entrainer: Manufacture specification 0.15fl.oz/1% air/100 lb cement.

 Coarse aggregate: 2 in nominal maximum size, crushed stone

 Bulk oven-dry specific gravity = 2.573, Absorption = 0.1%

 Oven-dry rodded density = 120 pcf

 Moisture content = 1%

 Fine aggregate: Natural sand

 Bulk oven-dry specific gravity = 2.54, Absorption = 0.2%

 Moisture content = 3.67%

 Fineness modulus = 2.68

Design the concrete mix according to the following conditions:

Design Environment

 Building frame

 Required design strength = 27.6 MPa

 Minimum dimension = 150 mm

 Minimum space between rebar = 40 mm

 Minimum cover over rebar = 40 mm

 Statistical data indicate a standard deviation of compressive strength of 2.1 MPa is expected

(more than 30 samples).

 Only air entrainer is allowed.

Available Materials

 Air entrainer: Manufacture specification 6.3 ml/1% air/100 kg cement.

 Coarse aggregate: 19 mm nominal maximum size, river gravel (rounded)

 Bulk oven-dry specific gravity = 2.55, Absorption = 0.3%

 Oven-dry rodded density = 1761 kg/m3

 Moisture content = 2.5%

 Fine aggregate: Natural sand

 Bulk oven-dry specific gravity = 2.659, Absorption = 0.5%

 Moisture content = 2%

 Fineness modulus = 2.47

Using the following data for an unreinforced PCC Pavement slab, find the following:

 Design strength f’c = 4,000 psi

 Slab thickness = 12”

 Standard deviation f’c of obtained from 20 samples = 200 psi

 Ignore any exposure requirement

 Use air entrained concrete

 Fineness modulus of fine aggregate = 2.60

 Maximum aggregate size = 2” and nominal maximum aggregate size = 1.5”

 Bulk oven-dry specific gravity of coarse aggregate = 2.6

 Oven-dry rodded density of coarse aggregate = 125 pcf

a. required compressive strength

b. water-cement ratio

c. Coarse aggregate amount

d. If the w/c ratio is 10% reduced, will the quantity of coarse aggregate increase, decrease or remain

the same? Explain your answer.

A project specifies a concrete strength of at least 3000 psi. Materials engineers will design the mix for

a strength higher than that. Calculate the required average compressive strength of the mix design if

the standard deviation is s = 350 psi. Estimate the modulus of elasticity of the concrete at the required

average compressive strength (the calculated strength, not the given strength).

The design engineer specifies a concrete strength of 5500 psi. Determine the required average

compressive strength for

a. a new plant where s is unknown

b. a plant where s = 500 psi for 22 test results

c. a plant with extensive history of producing concrete with s = 400 psi

d. a plant with extensive history of producing concrete with s = 600 psi

A beam ABC with an overhang at one end

supports a uniform load of intensity 12 kN/m and a

concentrated moment of magnitude 3 kN . m at C

(see figure).

Draw the shear-force and bending-moment

diagrams for this beam.

The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 780 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20 kg/m3

Converting Bearings to Azimuth

1. AB, DUE NORTH

2. BS, S75°25'W

3. GE, N0°54'W

4. IO, S50°50'E

5. AC, N27°35'E

6. XY, DUE WEST

7. YZ, N25°75'E

8. WX, S80°54'E

9. UV,S10°50'W

10. ST, DUE EAST

Converting Azimuth to Bearing

1. Azim of Line DE = 228° 15'

2. Azim of Line EF = 135° 00'

3. Azim of Line DE = 0°

4. Azim of Line EF = 357° 59'

5. Azim of Line CD = 70° 30'

6. Azim of Line DE = 90°

7. Azim of Line EF = 135° 00'

8. Azim of Line DE = 200° 09'

9. Azim of Line EF = 37° 19'