Posts Tagged ‘CE Board Exam Nov. 2003’
The 3kg slider is released from rest at point A and slides with negligible friction in a vertical plane along the circular rod. The attached spring has a stiffness of 350 N/m and has an unstretched length of 0.75m.
1) Which of the following gives the gravitational potential energy if the slider passes position B.
2) Which of the following gives the elastic potential energy if the slider passes position B.
3) Which of the following gives the velocity of slider as it passes position B.
Solution:
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The block of mass m = 1.6kg slides along the horizontal rough plane shown in the figure. The position coordinate x is measures from the under formed position of the ideal spring, which has stiffness of K = 30 N/m. at x = 0 the block is initially moving to the right with speed V1 = 6m/s.
1) Which of the following gives the value of x when the block first comes to rest.
2) Which of the following gives the acceleration of the block upon reaching the distance x.
3) Which of the following gives the speed of block when it reaches x = 0 for the second time.
Solution:
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The lower ends of the three bars in the figure are at the same level before the rigid homogeneous 18Mg block is attached. Each steel bar has an area of 600mm2 and E = 200 GPa. For the bronze bar, the area is 900mm2 and E = 83 GPa.
1) Which of the following gives the stress developed in the bronze bar.
2) Which of the following gives the stress developed in the steel bar.
3) Which of the following gives the elongation of the bars.
Solution:
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From a figure shown shows a square isolated reinforced concrete column and footing with the corresponding reinforcements. The foundation is strong enough that form works is not required for footing.
Unit weight of bars is 7860 kg/m3.
1) Compute the weight of 16mmØ bars in kg/m.
2) Compute the length of 16mmØ bars in meters.
3) Compute the quantity of 16mmØ bars in kg (mass).
Solution:
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For purposes of implementing rules and regulations of P.D. 1594 and unbalanced bid shall be defined as a bid containing one or more pay items that are 30% higher than the unit AGE (Approved Gov’t. Estimate) in respect to major items whereas other pay items are priced lower than the unit AGE, major items being defined as pay items representing at least 20% of the AAE or the first two items having the highest percentage of the AAE(Approved Agency Estimate) or those indicated or specified in the instruction to bidders. If the AAE of the Gov’t Project is 15M.
1) Which of the following gives the cost of an item to be automatically considered a major item?
2) If the pay item has a bid quantity of 4000 units and a unit price of P1000, which of the following gives the total cost of the item?
3) If there is a quantity overrun of 25% of the item mentioned in the second problem without any change in the unit cost, what is the change order quantity?
Solution:
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From the given figure shown:
1) Which of following gives the reaction at C.
2) Which of following gives the shear at a distance of 7m. from A.
3) Which of following gives the moment at a distance of 3m. from A.
Solution:
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A rectangular reinforce concrete beam has a width of 250mm, a total depth of 600mm, and an effective depth of 500mm. It is reinforced with 3-25mmØ. Fc’ = 28MPa and fy = 415MPa. The beam is carrying a slab 150mm thick, 5m. wide. The beam has a span of 6m. If the unit weight of concrete is 24kN/m3.
1) Which of the following gives the unfactored dead load acting on the beam?
2) Which of the following gives the ultimate moment capacity of the beam?
3) Which of the following gives the unfactored live load that the beam could support?
Solution:
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Section 4.5.1.4.5 of the 1992 National Structural Code of the Philippines gives the allowable stresses, in MegaPascals, for beams not restrained against latreal buckling as follows:
1) Tensio:
Fb = 0.60Fv
2) Compression:
The larger value computed by Formula (4.5-6a) or (4.5-6b) and (4.5-7) as applicable, but not more than 0.60Fv
Or, when the compression flange is solid and approximately rectangular in cross-section and its area is not less than that of the tension flange:
Where Cb = 1.75 + 1.05(M1/M2) + 0.30(M1/M2)2 but more than 2.3, where M1 is the smaller and M2 the larger bending moment at the ends of the unbraced length, taken about the strong axis of the members, and where M1/M2 the ratio of end moments, is positive when M1 and M2 have the same sign (reverse curvature bending) and negative when they are of opposite sighs (single curvature bending). When the bending moment at any point within an unbraced length is larger than that at both ends of this length, the value of Cb shall be taken as unity for cantilever beams and rt is the radius of gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web, and
d = Beam Depth
bf = Flange Width
tf = Flange thickness
A steel beam having a simple span of 8m. is subjected to a moment M at the left end and 25% of M at the right end. The steel section has the following properties.
Fv = 248MPa
rt = 0.053m.
d = 0.533m.
bf = 0.210m
tf = 0.016m.
Sx = 0.002077m3
1) Which of the following gives the max. slenderness ratio above which is considered a short beam.
2) Which of the following gives the allowable bending stress in the compression force.
3) Which of the following gives the moment at the left end.
Solution:
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A rectangular wooden beam has a span of 6m. and carries a total uniform load of 25kN/m including its own weight. The beam is made up of 80% stress grade Apitong with allowable stresses shown on table TM-6.
Allowable stress for Apitong 80% Stress Grade:
Allowable bending = 16.5 MPa Compression parallel to grain = 9,56 MPa
Compression perpendicular to grain = 2.20MPa
Shear parallel to grain = 1.73 MPa
Modulus of elasticity = 7310 MPa
1) Which of the following gives the smallest dimension of beam that will not exceed the allowable bending stress.
2) Which of the following gives the smallest dimension of the beam that will not exceed the allowable shearing stress.
3) Which of the following gives the smallest dimension of the beam that will not exceed the allowable deflection.
Allowable deflection = L/240
Solution:
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A built up section is made up of 3 rectangular plates welded to form an H-beam. The overall depth is 400mm and is 13 meters long. The slenderness ratio L/r = 200. The max. load in tension is 1600 kN and a min. load in compression is 260kN. The member is to carry a load P = max load + ½ min. load.
1) Compute the required area of the section if allowable stress is 185MPa.
2) Compute the width of the flange if r = ¼ width of flange.
3) Compute the thickness of the plate.
Solution:
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From the figure shown, the following data are given:
| D |
4 |
inches |
| H1 |
0.2 |
ft |
| K1 |
0.0038 |
ft/min |
| h = 1.25ft. |
| d = 1.5 inches |
| H2 = 0.3 ft. |
| K2 = 0.00075 ft/min. |
| Total H = H1 + H2 = 0.5 ft. |
1) Determine the total flow of water q.
2) Find the equivalent value of K1, for both annual and inner ring
3) Determine the volume of water which percolate after 30 min in cm3
Solution:
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Three pipes A, B and C are connected in parallel. If the combined discharged of the 3 pipes is equal to 0.61 m3/s, and assuming they have equal values of friction factor “f”, compute the following using the tabulated data shown.
PIPELINE LENGTH DIAM.
A 600 m. 150 m.
B 480 m. 200 m.
A 750 m. 100 m.
1) Compute the rate of flow of pipeline A in li/sec.
2) Compute the rate of flow of pipeline B in li/sec.
3) Compute the rate of flow of pipeline C in li/sec.
Solution:
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From the results of sieve analysis and the grain size curves for soils 1 and 2.
1) Compute the value of uniformity coefficient Cu.
2) Classify soil No. 1 using USCS Method.
3) Classify soil No. 2 using USCS Method.
Soils 1 and 2
| SIEVE ANALYSIS |
| Sieve Number |
Diameter mm |
Percent Passing % |
| Soils 1 |
Soils 2 |
| 4 |
4.760 |
100 |
90 |
| 8 |
2.380 |
99 |
64 |
| 10 |
2.000 |
98 |
58 |
| 20 |
0.850 |
92 |
35 |
| 40 |
0.425 |
70 |
22 |
| 60 |
0.250 |
46 |
15 |
| 100 |
0.150 |
25 |
10 |
| 200 |
0.074 |
0 |
4 |
| |
|
|
|
————–
Solution:
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A retaining wall 8m. high is supporting a horizontal back fill having a dry unit weight of 1600 kg/m3. The cohesion less soil has an angle of friction of 33°.
1) Compute the Rankine active force on the wall.
2) Compute the Rankine active force on the wall if the water table is located at a depth of 3.5m. below the ground surface. The saturated unit weight is 18.7 kN/m3.
3) Compute the location of the resultant active force from the bottom for the second condition.
Solution:
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A piece of wood floats in water with 50 mm projecting above the water surface. When placed in glycerine of sp.gr. 1.35, the block projects 75 mm above the liquid surface.
1) Find the height of the piece of wood.
2) Find the sp.gr. of wood.
3) Find the weight of the wood if it has a cross sectional area of 200 mm x 200 mm.
Solution:
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A reservoir of glycerine has a mass of 1200kg and a volume of 0.952 m3.
1) Find its weight in kN.
2) Find its specific weight.
3) Find its specific gravity.
Solution:
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From the given soil profile shown, the ground surface is subjected to a uniform increase in vertical pressure of 12 N/cm2.
1) Compute the buoyant unit weight of clay.
2) Compute the overburden pressure Po of mid-height of the compressible clay layer.
3) Compute the total settlement due to primary consolidation.
Solution:
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Saturated clay having a thickness of 20m. has a void ratio of 0.68 and a specific gravity of 2.7.
1) Compute the density of clay.
2) Compute the total vertical stress at the bottom.
3) Compute the effective stress at the bottom.
Solution:
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The total weight of soil when saturated 1526g and the weight of the soil after drying is 1053g. If the specific gravity of soil is 2.84.
1) Compute the moisture content.
2) Compute the void ratio.
3) Compute the porosity.
Solution:
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February 23rd, 2010
admin
A cylindrical tank 4m. in diameter and 6m. high is filled with water. It is tilted to a position enough for the water surface to cut the diameter of the base.
1) How much water retained in the tank.
2) If the tank is placed in vertical upright position, how deep is the water in the tank.
3) How fast in rpm could the tank be rotated about its vertical axis so that the depth of water at the center is zero.
Solution:
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February 23rd, 2010
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A wooden storage vat full of oil sp.gr. = 0.80 is in the form of a frustum of a cone, 2m. diameter at the top and 4 meters diam. at the bottom and 3m. high. It is provided with 2 steel hoops, one at the top and one at the bottom.
1) Compute the hydrostatic force on the side of the container.
2) How high is the said force above the bottom?
3) Compute the force in the bottom hoop.
Solution:
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February 23rd, 2010
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Water flows through an almost level channel 30m. wide at 12 m3/s. The depth gradually increases form 1.0m. to 1.1m. for a length of flow of 5m.
1) What is the head loss?
2) What is the slope of the energy gradient.
3) Compute the value of the roughness coefficient.
Solution:
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February 22nd, 2010
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The sum of two numbers is K. The product of one by the cube of the other is to be a maximum. What is one of the numbers?
Solution:
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February 22nd, 2010
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Find the volume of the spherical wedge having a radius of 2m. and a central angle of 1.25 rads.
Solution:
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February 22nd, 2010
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Round off to 4 significant figures 102.48876
Solution:
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February 22nd, 2010
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A closed traverse of a triangular lot is tabulated as shown:
LINES BEARING DISTANCE
AB N. 60° E. 1000 m.
BC Due South ——
CA N. 60° W. ——
An area of 280000 m2 is cut from point A to the line BC. Find the length of the dividing line from A.
Solution:
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February 22nd, 2010
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Find the length of curve defined by the polar equation r = 4 (1 – Sin θ)
Solution:
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February 22nd, 2010
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From the given cross-section notes of an earthworks having an area of 33.1 m2, compute the value of x if it has a side slope of 2:1 Width of roadway is 10m.
Solution:
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February 22nd, 2010
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A right circular cone has a surface area of 386 sq.cm. Its daim. Is ½ of its altitude. What is its altitude?
Solution:
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February 21st, 2010
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In triangle MNO, MN = 4.25cm, NO = 961cm. and OM = 8.62cm. A rectangle is inscribed in it such that its shorter side is on the 4.25cm. side of the triangle. Find the max. area of the rectangle.
Solution:
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February 21st, 2010
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What is the area bounded by the curve y = 6 Cos x and the x-axis from x = π/2, solve by integration.
Solution:
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February 21st, 2010
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Compute angle A if B =81°50’, C = 94°30’ for a spherical triangle whose side c = 90°.
Solution:
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February 21st, 2010
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When the expression x4 + ax3 + 5x2 + bx + 6 is divided by (x – 2) the remainder is 16. When it is divided by (x + 1) the remainder is 10. Find the value of constant b.
Solution:
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February 21st, 2010
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A machine bought at P420,000 has an economic life of 6yrs. with a salvage value of P50,000.00. Cost of money is 12% per year. The first year depreciation is found to be P105,714.00. What method of depreciation is used?
Solution:
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