Civil Engineering Online Review

A simple curve of the proposed extension of Mantabahadra Highway have a direction of tangent AB which is due north and tangent BC bearing N.50°E. Point A is at the P.C. whose stationing is 20 + 130.46. The degree of curve is 4°.

1  Compute the long chord of the curve.

2  Compute the stationing of point D on the curve along a line joining the center of **the curve which makes an angle of 54° with the tangent line passing thru the P.C.

3  What is the length of the line from D to the intersection of the tangent AB.

Solution:

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A simple curve has a central angle of 36° and a degree of curve of 6°.

1  Find the nearest distance from the mid point of the curve to the point of **intersection of the tangents.

2  Compute the distance from the mid point of the curve to the mid point of the long **chord joining the point of curvature and point of tangency.

3  If the stationing of the point of curvature is at 10 + 020, compute the stationing of **a point on the curve which intersects with the line making a deflection angle of 8° **with the tangent through the P.C.

Solution:

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Given the equation of ellipse as 25x² + 4y² = 100

1  Find the equation of the diameter of ellipse which bisects chords having a slope of **½.

2  Find the slope of the curve at point(1.2, 4).

3  Find the perimeter of the curve.

Solution:

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The max. area of the parabola inscribed in a right circular cone having a diameter of 24cm. is equal to 207.8 cm³.

1  Compute the base of the parabola inscribed in a right circular cone.

2  Compute the height of the parabola of max. area.

3  Compute the volume of the right circular cone.

Solution:

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Two sets of students are collecting traffic data at the two sections A and B of a highway 200m. apart. Observation at A shows that 5 vehicles passes that section at intervals of 8.18sec., 9.09sec., 10.23sec., 11.68sec., and 13.64sec., respectively. If the speeds of the vehicles were 80, 72, 64, 56 and 48 kph respectively.

1  Compute the density of traffic in vehicles per km.

2  Compute the time mean speed in kph.

3  Compute the space mean speed in kph.

Solution:

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An area of 50,977.84 sq.m. is to be segregated from a triangular  lot ABC with one of its sides BC equal to 400m. and the boundary of this segregated area DEBC has side DE parallel to BC. The length of the side DE is equal to 150m. and the angle ABC is 50°.

1  At what angle is the side AC making with side BC?

2  What is the area of the whole lot?

3  What is the area of section ADE?

Solution:

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Given the equation of he curve y = 0.10 (1600 – x²)

1  Compute the area bounded by the curve and the x-axis.

2  Compute the moment of inertia with respect to y-axis

3  Compute the radius of gyration with respect to the y-axis.

Solution:

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A right circular cylinder is inscribed in a right circular cone of radius 6cm.

1  Find the radius of the cylinder if its volume is maximum.

2  Find the max. volume if the altitude is 12cm.

3  Find the radius of the radius of the cylinder if its lateral area is maximum.

Solution:

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From the given data of a closed traversed, compute the following.

1  Bearing of line DA.

2  Distance of line DA.

3  Area of lot ABCD in acres.

LINE              BEARING           DISTANCE

AB                 S.8°51’W.             126.90 m.

BC                 N.18°51’W.             90.20 m.

CD                 N.32°27’3.            110.80 m.

DA                 ————-         ————

Solution:

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To prepare for his retirement at a certain period “n” years from now, a self employed engineer deposits a uniform amount of P2500 at the  end of each year into a fund that earns an interest of 2.5% compounded annually.

1  Find the value of “n” when the compound amount factor due to the series of equal **deposits (annuity) is equal to 25.5447.

2  How much is the worth of the fund at the end of ”nth” year?

3  If he wants to retire in 8 yrs, how much will be the worth of his deposits at this **time?

Solution:

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Given:

STATION           ELEV.(m)           DISTANCE(km)

Alpha                  680 m.               Alpha to Bravo= 12 km

Bravo                  645 m.               Bravo to Charlie= 15 km

Charlie               620 m.

1  Compute the elevation of the line of sight at station Bravo with the instrument **placed at station Alpha such that station Charlie would be visible from station **Alpha considering the effect of curvature and refraction correction.

2  Assuming that station Bravo will obstruct the line of sight from station Alpha while **observing station Charlie and a 4m. tower is constructed on top of station Bravo. **Compute the height of equal towers at stations Alpha and Charlie in order that the **three stations as observed from station Alpha will still be intervisible.

3  Without constructing any tower at station Bravo, what height of tower must be **constructed at station Charlie so that both station Bravo and Charlie would be **visible from station Alpha.

Solution:

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The tenth term of a G.P. is 39366 and the 4^th term is 54.

1   Find the common ratio.

2   Find the first term.

3   Find the 7^th term.

Solution:

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The equation of ellipse is given as 16x² + 36y² = 576.

1   Compute the equation of polar of the point (4, -6) with respect to the ellipse.

2   Compute the equation of the diameter of ellipse which bisects all chords having a ***slope of 3.

3    Compute the second eccentricity of the ellipse.

Solution:

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Two identical closed conical tanks contains equal amount of liquid. The first tanks horizontal base is at the bottom while that of the second is at the top. The liquid in the first tank stands 3m. deep.

1   What is the volume of the liquid in the 2^nd tank?

2   How deep is the liquid in the second tank if its altitude is 6m. and the base radius ***is 2m?

3   If the unit weight of the liquid is 9100 N/m³, what is the weight of the liquid inside ***the tank in quintals?

Solution:

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A swimming pool is constructed in the shape of two overlapping identical circles having a radius of 9m. and each circle passes through center of each other.

1   Find the area common to the two circles.

2   Find the area of the swimming pool.

3   Find the perimeter of the swimming pool.

Solution:

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Find the area bounded by the curve x² – 10x + y² + 10y + 25 = 0

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Find the equation of the line whose slope is 2/3 and passes through the intersection of the lines x – 2y + 4 = 0 and 4x – 2y + 1 = 0.

Solution:

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x years from now, one investment plan will be generating profit at the rate (50 + x²) thousand pesos per year, while a second plan will be generating at the rate of (200 + 5x) thousand pesos per year. Find the total net excess profit if you invest in the second plan instead of the first plan up to the time the two plans yield equal profits.

Solution:

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Find the volume in the first octant, bounded by the surface x = 1 and x² = y + 2z.

Solution:

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A 1.2 tons car moving with a velocity of 30 kph bumps the rear of a 1.8 ton car moving in the same direction with a velocity of 20kph. The bumpers get locked during the collision. Determine the velocity of the cars immediately after impact.

Solution:

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A steel ball is projected upward from a level ground at an angle of 30° with the horizontal with a velocity of 300 m/s. When will it fall back to the ground in seconds.

Solution:

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The sides of triangle ABC are AB = 7cm., BC = 5cm. and CA = 9cm. Determine the width of the largest rectangle that can be inscribed in it such that the longer side of the rectangle is on the 9cm. side of the triangle.

Solution:

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Find the second derivative of y = x(x + 1)³ when x = 1.

Solution:

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Find the length of the latus rectum of 36x² + 9y² – 36 = 0.

Solution:

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In the given harmonic progression shown, compute the value of x:

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Find the value of E in the given equation:

Solution:

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A salesman started walking from office A at 8:30 A.M. at the rate of 2.5kph. He arrives at office B 12 seconds late. Had he started at A at 8:00 A.M. and walked at 1.5kph, he would have arrived at B one minute before the appointed time. At what time was he supposed to be at B.

Solution:

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A line level was run from point 5 to 6, 8km. apart. The average B.S. and also F.S. distance was 100m. At every turning point, the rod settles by 3cm. Find the total error in the recorded elevation of point 6.

Solution:

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A lot is bounded by 3 straight sides, namely: AB N.45°E, 160m. long, BC and CA 190m. long in clockwise direction. From point E, 100m. from A and on side AB, a dividing line runs to D which is on side CA. The area of ADE is to be 2/5 of the total area of the lot. Determine the length of DE if the total lot area is 11,643.88 sq.m.

Solution:

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A boy is entitled to 10 yearly endowments of P30,000 each starting at the end of 11^th year from now. Using an interest rate of 8% compounded annually, what is the value of this endowment now?

Solution:

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A factory has production capacity of 4000 units per moth with an efficiency of 80%.

Fixed operating cost  P800,000 a month

Variable and material cost = P200/unit

Selling price per unit = P500

Find profit in pesos per moth.

Solution:

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Evaluate the integral of Cos⁷ 3x dx from 0 to π/6.

Solution:

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The upper and lower bases of a frustum of a regular rectangular pyramid are 3m x 4m and 6m x 8m respectively. If the volume is 140cu.m., what is the distance between the bases in meters?

Solution:

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A rectangular lot has a correct area of two hectares. Its length is trice its width. If the lengths of the sides were measured with a 50m. tape that is 0.02m. too long, compute the error in the area of the lot in square meters.

Solution:

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A downgrade of 3.2% meets a rising grade of 4.6% at station 73 + 180. Where the elevation is 998m. A sag curve, 440m. long, connects the gradelines from A at the downgrade to B at the upgrade. Find the elevation of B in meters.

Solution:

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