The beam shown in the figure carries a triangular load which varies from 12 kN/m at A to 0 at B and a concentrated load of 20kN at C.
1) Which of the following gives the nearest value of the reaction at B.
2) Which of the following gives the nearest value of the location of the point of inflection from A.
3) Which of the following gives the nearest value of the maximum positive moment.
Solution:
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The bridge truss shown on the figure carries a concentrated load of 20kN and a uniform load of 2 kN/m.
1) Which of the following gives the nearest value of the max. ordinate of the influence diagram for member BG?
2) Which of the following gives the nearest value of the maximum tensile force of member BG?
3) Which of the following gives the nearest value of the maximum compressive force of the member BG?
Solution:
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A curvilinear motion of a particle is defined by Vx = 40 – 15t and y = 75 – 3t2, where Vx is in meters per second, y is in meters and t is in seconds. It is also known that x = 0 when t = 0.
1) Which of the following gives the nearest value of the second value of time “t” when “x” will be equal to 0?
2) Which of the following gives the nearest value of the velocity when x = 0 at the second value of time?
3) Which of the following gives the nearest value of the acceleration when x =0 at the second value of time?
Solution:
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A rectangular reinforced concrete beam has a width b = 300mm and effective depth d = 400mm. If fc’ = 28MPa, fy = 280MPa and Es = 200,000MPa.
1) Which of the following gives the nearest value of the distance of the N.A. form the top of the beam so that the strain in concrete εc = 0.003 will be attained at the same time with the yield strain of steel εy?
2) Which of the following gives the nearest value of the total compressive force of concrete?
3) Which of the following gives the nearest value of the balanced steel ratio.
Solution:
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A cover plated beam consist of a W 21 x 62 with 12mm x 300mm plates attached to the top and bottom of the flange and is fastened by two rows of 20mmØ rivets. The beam has it simple span of 6m. and carries a uniform load of 270 kN/m.
d = 0.560 m.
Ix = 0.00151 m4
1) Which of the following gives the nearest value of the distance form the N.A. to the centroid of the cover plate?
2) Which of the following gives the nearest value of the moment of inertia of the built up section about the N.A.?
3) Which of the following gives the nearest value of the pitch of rivets (P) if the capacity of each rivet is 30 kN?
Where:
I = moment of inertia about N.A.
R = shear capacity of rivet
V = shear force at the point where the pitch is required
A = area of cover plate
γ = distance from N.A. to the centroid of cover plate
P = pitch of rivets
Solution:
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The figure shows a train traveling at a constant uniform velocity of 75kph and a car travelling at a speed of 36kph towards point 0.
1) If the train moves at a uniform velocity, which of the following gives nearest value of the required time(t) for the train to reach the point of collision(point 0).
2) Which of the following gives the nearest value of the acceleration of the car, if the car reaches point 0, 10 seconds ahead than that of the train.
3) Using the acceleration computed above, which of the following gives the nearest value of the velocity of the car at the collision point.
Solution:
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A certain project requires a total volume of concrete of 2000m3 and needs:
Pump ……….P500/hr rental.
Pump capacity ………..100 m3/day
Working hours of pump …… 8hrs/day
6 laborers @ P35/hr.
4 Carpenters @ P40/hr.
2 Finishers @ P45/hr.
1 Operator @ P50/hr.
1) Which of the following gives the nearest value of the number of working hours to complete the project?
2) Which of the following gives the total cost of the project?
3) Which of the following gives the unit cost (per cu.m.) of the project?
Solution:
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The implementing rules and regulation of P.D. Decree No. 1594 states that no award of contract shall be made to a bider whose bid price is higher than the (AGE) Allowable Government Estimate or the (AAE) Approved Agency Estimate Whichever is higher, or lower than 70% of the AGE. The Allowable Gov’t. Estimate(AGE) is defined as one half the sum of the (AAE) and the average of all responsive bids. For the purposes of determining the average of responsive bids, bids higher than 120% of the AAE or lower than 60% of AAE shall not be considered.
The approved agency estimate (AAE) of a Government project is 2 million. The bids are:
| Bidder |
Bid Price (M) |
| A |
2.65 |
| B |
2.4 |
| C |
1.85 |
| D |
1.17 |
| E |
1.23 |
| F |
2.24 |
| G |
2.34 |
| H |
2.18 |
1) Which of the following are considered responsive bidders?
2) Which of the following gives the nearest value of the average responsive bidders?
3) Which of the following gives the nearest value of the allowable government estimate (AGE)?
Solution:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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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:
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