A non-prismatic beam AB is shown. The beam is fixed at B and hinged at A. The beam is loaded with a concentrated moment at A causing a 1-radian rotation at A.
1. Which of the following gives the value of the moments at A.
A. 530EI/1101
B. 532EI/1201
C. 520EI/1301
D. 540EI/1111
2. Which of the following gives the vertical reaction at A.
A. 73EI/1301
B. 96EI/1101
C. 75EI/1111
D. 87EI/1201
3. Which of the following gives the ratio of the moment at B and moment at A.
A. 169/266
B. 185/456
C. 184/385
D. 132/541
Solution:
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For the cable shown
1. Which of the following most nearly gives the tension in segment CD, in KiloNewton:
A. 7.3
B. 6.8
C. 5.2
D. 6.9
2. Which of the following most nearly gives the tension in segment AB, in KiloNewton:
A. 6.8
B. 5.2
C. 6.9
D. 7.3
3. Which of the following most nearly gives the value of h in meters:
A. 2.74
B. 2.57
C. 2.32
D. 3.12
Solution:
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The coplanar force system shown consists of two forces and a couple. All coordinates are in meters.
1. Which of the following most nearly gives the resultant of the force system in Newtons.
A. 16.8
B.14.3
C. 12.2
D. 13.1
2. Which of the following most nearly gives the angle that the resultant forces make with the horizontal axis in degrees (positive counterclockwise)?
A. 72.4
B. 55.2
C. 68.9
D. 65.2
3. Which of the following most nearly gives the y-intercept of the resultant force in meters.
A. 3.14
B. 6.38
C. 2.46
D. 5.34
Solution:
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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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A wooden purlin is used on a truss with a top chord inclined at 30° with the horizontal. The purlin is 50mm x 100mm and has length of 3.5m spaced by 0.45m. on center. It carries a live load of 750Pa, weight of rooling is 120 Pa and ceiling load equal to 140 Pa. Using Apitong.
1) Which of the following gives the uniform load carried by the purlin is N/m?
2) Which of the following give the maximum flexural stress.
3) Which of the following gives the vertical deflection of the purlin.
Solution:
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A beam having a value of EI equal to 100,000 kN.m2 is loaded as shown.
1) Which of the following gives the deflection at the mid span if the middle support is removed.
2) Which of the following give the deflection at the mid span due to a unit load upward if the middle support is removed.
3) Which of the following gives the reaction at the middle support.
Solution:
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A 3 meter wide wall footing supports a 300mm wall. It is reinforced with 25mm diameter bars with concrete converging of 75mm. Strength of concrete is 21MPa, Fy = 415MPa
1) Which of the following gives the available space for development?
2) Which of the following gives the development length required development length required by the code?
3) When the required development length is smaller than the space available for development, the practice is to increase the bar diameter and spacing of the bars. Which of the following gives the maximum diameter to be used?
Solution:
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A contractor wish to buy a machine worth 1 million after one year. If the bank gives an interest of 1.5% compounded monthly.
1) What single amount must be deposit now in order to have the desired amount after one year?
2) What amount must he deposit at the bank at every beginning of the month in order to have 1 million after one year?
3) If he deposits P100,000 at the beginning of each month for 6 months starting 6 months from now, how much more will the contractor has to have to buy the machine?
Solution:
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The beam shown weighs 30N/m.
1) Which of the following gives the tension force?
2) Which of the following gives the reaction at the pinned support?
3) Which of the following gives the angle that the reaction makes with the horizontal measured in counterclockwise direction.
Solution:
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A beam is loaded as shown on the figure.
1) Which of the following gives the reaction at A?
2) Which of the following gives the maximum shear?
3) Which of the following gives the maximum moment?
Solution:
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A rigid block weighing 176.4 kN is attached as shown on the figure. If the block is to remain horizontal.
1) Which of the following gives the ratio of the load carried by each load?
2) Which of the following gives the stress of the bronze?
3) Which of the following gives the elongation of the rods?
Solution:
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A simply supported steel beam carries a uniform concrete slab 200mm thick. It carries a ceiling load of 500 Pa and live load pressure equal to 2000Pa. The length of the beam is 6meters and is spaced at 2m. on centers. Unit weight of concrete is 24kN/m2. Allowable bending stress for steel beam is 0.66Fy. Modulus of elasticity is 200GPa. Fy = 248MPa.
1) Which of the following gives the uniform load pressure carried by the beam?
2) Which of the following gives the load carried by the beam in kN/m?
3) Which of the following gives the most economical section?
| Section |
Moment of Inertia |
Depth |
| W 12 x 26 |
0.0000849 m4 |
0.310 m. |
| W 12 x 19 |
0.0000541 m4 |
0.309 m. |
| W 12 x 14 |
0.0000369 m4 |
0.302 m. |
Solution:
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A village has 3 alternatives to choose from in replacing the existing piping system. A pump is required and is estimated to last for 10 years. Replacement will be for 30 years project. Pipes will be installed will last for 30 years. At an interest of 15%.
| Alternative |
One |
Two |
Three |
| Pump |
300,000 |
600,000 |
1,200,000 |
| Pipe |
600,000 |
600,000 |
400,000 |
| Annual maintenance |
240,000 |
180,000 |
120,000 |
1) Which of the following gives the present value of alternative one?
2) Which of the following gives the present value of alternative two?
3) Which of the following gives the best option?
Solution:
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Compound shaft shown is attached to rigid supports.
For the bronze segment AB:
Diameter = 75mm
G = 35GPa
τ = 60MPa
For steel segment BC:
Diameter = 50mm
G = 83GPa
τ = 80MPa
1) Which of the following gives the ratio of b/a so that each material will be stressed to its max. permissible limit.
2) Which of the following gives the reaction at A.
3) Which of the following gives the max. angle of twist when a = 1m.
Solution:
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From the given figure shown.
1) Which of the following gives the deviation of B relative to the tangent drawn at A.
2) Which of the following gives the deviation at D relative to the tangent drawn at A.
3) Which of the following gives the deflection at D.
Solution:
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A tied column having the given cross section shown is reinforced with six-32mmØ bars.
fc’ = 21MPa
fy = 415MPa
1) Which of the following gives the reinforcement ratio in percent?
2) Which of the following gives the ratio of e/h if the eccentricity is 250mm?
3) Which of the following gives the value of the max. load Pn that the column could carry using the interaction diagram?
Solution:
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The implementing rules and regulations of P.D. 1594 states that no award of contract shall be made to a bidder whose bid price is higher than the allowable government estimate (AGE) or the Approved Agency Estimate (AAE), whichever is higher, or lower than seventy percent (70%) of the AGE. The AGE shall be equal to one half of the sum of the AAE and the average of all responsive bids. For purposes of determining the average of all responsive bids, bids higher than one hundred twenty percent (120%) of the AAE or lower than sixty percent (60%) of the AAE shall not be considered. An unbalanced bid shall be defined as a bid containing one or more pay items that are thirty percent (30%) higher than the unit AGE in respect to major items whereas other pay items being defined as pay items representing at least twenty percent (20%) of the AAE or the first two items having the highest percentage of the AAE or those indicated/specified in the instructions to Bidders.
The itemized AAE and Bids for a project are as follows:
| |
Bids |
| Item |
AAE |
Bidder A |
Bidder B |
Bidder C |
| 1 |
3000 |
2800 |
2500 |
2000 |
| 2 |
8000 |
10800 |
9000 |
6000 |
| 3 |
15000 |
12000 |
16000 |
20000 |
| 4 |
6000 |
5500 |
5500 |
5000 |
| 5 |
7500 |
7000 |
8000 |
6000 |
| 6 |
2500 |
3000 |
2800 |
1800 |
| 7 |
1500 |
2000 |
1600 |
1200 |
| 8 |
2000 |
2000 |
1800 |
1600 |
1) Which of the following gives the min. value of bid to be automatically considered as major item?
2) What are the major items?
3) Which of the following are the balance bid?
Solution:
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A 4m length pipe having a diam. of 600 mm is to be installed in one hour at a cost of P570/m. 1 foreman has a rate of P50/hr, 2 skilled laborers has a rate of P35/hr. A backhoe was rented for P800/hr and a compactor was rented at a rate of P120/hr.
Volume of cement needed is 0.07m3
at P130 per cu.m.
Volume of sand needed is 0.15m3
at P300 per cu.m.
Vat is 10% of equipment, labor and material cost.
Insurance is 30% of equipment and material cost.
1) Which of the following gives the total cost of labor and equipment per meter length of pipe.
2) Which of the following gives the cost of material per meter length of pipe.
3) Which of the following gives the total cost of the project per meter length.
Solution:
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