From the figure shown.
1) Which of the following gives the influence diagram for reaction at B?
2) Which of the following gives the influence diagram for shear at C?
3) Which of the following gives the influence diagram for moment at C?
a) Influence Diagram for Reaction at B
b) Influence Diagram for Shear at C
c) Influence Diagram for Moment at C
Solution:
A riveted bracket is subjected to a load P acting at an angle of θ from the vertical. There are 4 – 25mmØ rivets, two on each column flange and two plates, one on each column flange.
1) Which of the following gives the max. shear stress if P = 40kN, θ = 45°, b = 100mm, a = 150mm and e = 250mm.
2) Which of the following gives the maximum value of P if e = 250mm and the allowable shearing stress is 120MPa?
3) Which of the following gives the minimum eccentricity “e” when P = 40kN if the allowable shearing stress is 120MPa?
Solution:
A concurrent force system in space is composed of 3 forces described as follows. P12 has a magnitude of 93kN and acts through the origin and point x = 5, y = -4 and z = -6. has a magnitude of 126kN and acts through the origin and point x = -1, y = 5 and z = +3. PP3 has a magnitude of 38kN and acts through the origin and point x = 4, y =1 and z = 3.
1) Which of the following gives the x-component of the resultant of the sets of forces?
2) Which of the following gives the y-component of the resultant of the sets of forces?
3) Which of the following gives the resultant of the sets of forces.?
Solution:
A reinforced concrete beam has a width of 420mm and an effective depth of 640mm. It has a simple span of 5.75m. It carries a uniform dead load of 72 kN/m and a live load of 84kN/m fc’ = 27.6 MPa.
1) Which of the following gives the value of the factored uniform load?
2) Which of the following gives the ultimate shear force Vu of concrete in kN?
3) Which of the following gives the shearing force to be resisted by the stirrups?
Solution:
The implementing rules and regulations of PD 1594 states that for a unit price contract, quantity overruns or underruns of not more than 15% of the estimates per major pay item and 25% per minor item need not be covered by a change order provided that the same is authorized by the approving authority of the contract. The quantities and unit prices of a project are as follows:
| Item | Quantity | AAE
Unit Price |
Contract
Unit Price |
| 1 | 100 | 7000 | 8000 |
| 2 | 200 | 5500 | 6000 |
| 3 | 300 | 5000 | 4500 |
| 4 | 200 | 4000 | 3500 |
| 5 | 500 | 4800 | 5000 |
| 6 | 440 | 3500 | 4000 |
| 7 | 400 | 9000 | 10000 |
| 8 | 320 | 6000 | 5000 |
1) Determine the AAE of the project.
2) Determine the major items.
3) Determine the minimum increase in contract price if item 5 is covered by a change order.
Solution:
A steel shaft with a constant diameter of 60mm is loaded by torques applied as shown. Using G = 83GPa.
1) Which of the following gives the torque applied on the right side if the allowable shearing stress is not to exceed 23.58MPa?
2) Which of the following gives the reaction at the support?
3) Which of the following gives the angle of twist of the shaft?
Solution:
A simple beam 4.5 in span carries a concentrated load of 300 kN at its mid span and is subjected to an axial tensile force of 250kN. Fy = 248MPa.
Three sections are being considered as follows with their corresponding properties relevant to this problem.
| Section | Area | Beam
Depth |
Moment of
Inertia |
| W 42 x 55 | 0.01 m2 | 0.598 m | 0.000558 m4 |
| W 21 x 62 | 0.012 m2 | 0.533 m | 0.000554 m4 |
| W 21 x 68 | 0.013 m2 | 0.537 m | 0.000616 m4 |
1) Which of the following gives the lowest axial stress?
2) Which of the following gives the lowest bending stress?
3) Which of the following gives the safest section?
Solution:
Car A is moving east at 70 kph while car B is moving in the direction of N. 45° E. For a passenger in car A, B appears to be moving away in a direction of N. 30° W.
1) Which of the following gives the velocity of A in m/s?
2) Which of the following gives the velocity that B appears to the passenger in A?
3) Which of the following gives the true velocity of B?
Solution:
A two way reinforced concrete building floor system is composed of slab panels measuring 6.1m x 7.6m. in plan supported by shallow column line beams cast monolithically with the slab as shown. Thickness of slab is 180mm. The typical exterior panel carries a service line load of 6000Pa in addition to the self-weight of the floor. Assume unit weight of concrete to be 23 kN/m3. Beam BC has a dimension of 360 x 510mm. Use Direct Design Method
1) Which of the following gives the ultimate uniform load acting on the slab in kPa?
2) Which of the following gives the total static design moment for beam BC?
3) Which of the following gives the max. negative moment for beam BC?
Solution:
The figure shows a typical cross section of an isolated square footing. The swell factor for backfill is 1.20.
1) Which of the following gives the volume of excavation?
2) Which of the following gives the volume of gravel?
3) Which of the following gives the volume of backfill?
Solution:
A retaining wall 6m. high is supporting a horizontal backfill having a dry unit weight of 1600 kg/m3. The cohesionless soil has an angle of friction of 32° and a void ratio of 0.68.
1) Compute the Rankine active force on the wall.
2) Compute the Rankine active force on the wall if water logging occurs at a depth of 3.5m. from the ground surface.
3) Compute the location of the resultant active force from the bottom.
Solution:
Two footings rest in a layer of sand 2.7 m. thick. The bottom of the footing are 0.90m. below the ground surface. Beneath the sand layer is a 1.8m. clay layer. Beneath the clay layer is hard pan. The water table is at a depth of 1.8m. below the ground surface. Void ration of clay is 1.03.
1) Compute the stress increase at the center of clay layer assume that the pressure beneath the footing is spread at an angle of 2 vertical to 1 horizontal.
2) Determine the size of footing B so that the settlement in the clay layer is the same beneath footings A and B. Footing A is 1.5m. square.
3) Determine the settlement beneath footing A.
Solution:
A cohesionless soil has a friction angle of 30° and deviator stress of failure of 400 kPa.
1) Find the angle that the failure plane makes with the major principal plane.
2) Find the confining pressure.
3) Find shear stress at the point on the failure plane.
Solution:
A 0.36m. square prestressed concrete pile is to be driven in a clayey soil as shown in the figure. The design capacity of the pie is 360 kN, with a factor of safety of 2.
1) Compute the end bearing capacity of the pile.
2) Compute the skin friction expected to develop along the shaft of the pile.
3) Compute the length of the pile if α = 0.76.
Solution:
A 7m. deep braced cut in sand is shown. In the plan, the struts are placed at a spacing of 2m. center to center. Using Peck’s empirical pressure diagram, compute the following:
1) Strut load at level A
2) Strut load at level C
3) Strut load at level B
Solution:
A reservoir with a 3400 m2 area is underlain by layers of stratified soils as depicted in the figure.
1) Compute the average coefficient of permeability in m/hour.
2) Compute the interstitial velocity of water moving through the soil if it has a void ratio of 0.60. Express in cm/sec.
3) Compute the water loss from the reservoir in one year in cu.m. assuming that the pore pressure at the bottom sand layer is zero.
Solution:
Two reservoirs A and B have elevations of 250 m and 100m respectively. It is connected by a pipe having a diameter of 25 mm Ø and a length of 100m. A turbine is installed at point in between reservoirs A and B. If C = 120, compute the following if the discharge flowing in the pipe is 150 liters/sec.
1) Head loss of pipe due to friction.
2) The head extracted by the turbine.
3) The power generated by the turbine.
Solution:
A square plate having one of its side equal to 3.5 m. is immerse in a water surface in a vertical position such that the two edges of the square would be horizontal in order that the center of pressure shall be 12cm. from the center of gravity.
1) How far below the water surface should the upper plate be submerged?
2) What is the distance of the center of pressure from the water surface?
3) Determine the hydrostatic force acting on the plate at this position.
Solution:
A discharge of 750 liters/sec. flows through a pipe having a diameter of 400 mm Ø. Length of 65m. long, compute the head loss of the pipeline using:
1) Mannings Equation with n=0.013
2) Darcy Weishback formula with f = 0.012.
3) Hazen Williams Formula with C = 100.
Solution:
A stone weighs 468 N in air. When submerged in water if weighs 298N.
1) Find the volume of the stone.
2) Find the specific weight of the stone.
3) Find the specific gravity of the stone
Solution:
The area of a rhombus is 132 sq.cm. It has one diagonal equal to 12cm.
1 Determine the length of the other diagonal.
2 Determine the length of the sides of the rhombus.
3 Determine the acute angle between the sides of the rhombus.
Solution:
The vertical angle of the top of the flagpole as observed from point A is equal to 60°, and that of the bottom of the flagpole is 52°. The flagpole is placed on top of a pedestal. If the distance from A to the base of the pedestal is 14.20m.
1 Find the height of the pedestal
2 Find the height of the flagpole on top of the pedestal.
3 Find the distance from A to the top of the flagpole.
Solution:
It is estimated that between the hours of noon and 7:00 P.M. the speed of a highway traffic flowing past the intersection of EDSA and Ortigas Avenue in approximately
S = t3 – 9t2 +15t + 45 kph
Where “t” is the number of hours past noon.
1 At what time between noon and 7:00 P.M. is the traffic moving the fastest.
2 At what time between noon and 7:00 P.M. is the traffic moving the slowest.
3 What is the slowest speed it is moving at this time.
Solution:
A triangular corner lot has perpendicular sides of lengths 120m. and 160m. respectively.
1 Find the area of the largest rectangular bldg. that can be constructed on the lot ***with sides parallel to the street.
2 Find the perimeter that encloses the bldg.
3 If it cost P6000 per square meter of floor area of a bldg., how much would be the ***approximate cost if a three story bldg. is to be constructed.
Solution:
The equilateral hyperbola xy = 8 has the x-axis and y-axis as asymptote.
1 Determine the distance between the vertices.
2 Compute the length of the conjugate axis.
3 Compute the eccentricity of the hyperbola.
Solution:
For a nominal rate of 6% compounded semi-quarterly for 8years in an ordinary annuity, compute the following
1 Sinking fund factor.
2 Present worth factor.
3 Capital recovery factor.
Solution:
An ellipse has an equation of 9x2 + 16y2 = 144.
1 If the area enclosed by the ellipse on the first and 2nd quadrant is revolved about ***the x-axis, what is the volume generated.
2 What is the length of arc in the first quadrant of an ellipse.
3 What is the equation of the diameter of the ellipse which bisect all chords having a ***slope of 2.
Solution:
Compute the interest for an amount of P200,000 for a period of 8 yrs.
1 If it was made at a simple interest rate of 16%.
2 If it was made at 16% compounded bi-monthly.
3 If it was made at 16% compounded continuously.
Solution:
Given the technical description of a triangular lot.
LINES BEARING DISTANCE
AB N. 40° W. ?
BC N. 60° E. 810 m.
CA Due South ?
An area of 190,000 m2 is to be segregated along the side BC starting from B.
1 Compute the location of the other end of the dividing line BD along the side CA ***measured from C.
2 Compute the length of the diving line.
3 Compute the bearing of the dividing line from B.
Solution:
An easement curve has a length of spiral equal to 60m. having a central curve of a radius of 400m. The design velocity of the car allowed to pass thru this portion is 100kph.
1 Compute the rate of increase of centripetal acceleration.
2 If the friction factor is equal to 0.14, compute the super elevation rate in m/m ***width of roadway.
3 Compute the width of one lane of roadway if the difference in grade between the ***centerline and the edge of the roadway is 1/220.
Solution:
The peak hour factor for traffic during rush hour is equal to 0.60 with a highest 5min. volume of 250 vehicles. The space mean speed of the traffic is 90 kph.
1 Compute the flow of traffic in vehicles/hour.
2 Compute the density of traffic in vehicles/km.
3 Compute the max. spacing of the cars in meters.
Solution:
A line was determined to be 2395.25m. when measured with a 30m. steel tape supported throughout its length under a pull of 4kg at a mean temperature of 35°C. Tape used is of standard length of 20°C under a pull of 5kg. Cross-sectional area of tape is 0.03sq.cm. Coefficient of thermal expansion is 0.0000116°C. Modulus of elasticity of tape is 2 x 106 kg/cm3.
1 Determine the error of the tape due to change in temperature.
2 Determine the error due to tension.
3 Determine the corrected length of the line.
Solution:
The centerline of a proposed road cross section crosses a small valley between station 10 + 022 (elevation 123.00m.) and station 10 + 060 (elevation 122.50m.). The stationing at the bottom of the valley is 10 + 037 (elevation 111.2m.). The grade line of the proposed road passes the ground points at the edges of the valley (sta. 10 + 022) and (10 + 060) and the section at any of these stations are three level sections. Width of road base = 10m. with sideslope of 2:1. Assume that the sides of the valley slope directly to the lowest point from the edges.
1 Find the cross sectional area of fill at station 10 + 037.
2 Compute the volume of fill from station (10 + 022) to (10 + 037)
3 Compute the volume of fill from station (10 + 037) to (10 + 060).
Solution:
The tangents of a simple curve have bearings of N.20°E and N.80°E. respectively. The radius of the curve is 200m.
1 Compute the external distance of the curve.
2 Compute the middle ordinate of the curve.
3 Compute the stationing of point A on the curve having a deflection angle of 6° from ***the P.C. which is at 1 + 200.00.
Solution:
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