Civil Engineering Online Review

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:

F_b = 0.60F_v

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 0.60F_v

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 C_b = 1.75 + 1.05(M_1/M₂) + 0.30(M_1/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 M_1/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 C_b shall be taken as unity for cantilever beams and r_t 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

b_f = Flange Width

t_f = 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.

F_v = 248MPa

r_t = 0.053m.

d = 0.533m.

b_f = 0.210m

t_f = 0.016m.

S_x = 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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A plane truss as shown in the figure is acted upon by 480 N downward load at joints C and E and a 1200N load at J directed as shown.

1) Find the reaction at G.

2) Find the force acting on member AH.

3) Find the force acting on member JD.

Solution:

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The T-section shown is formed by joining two rectangular pieces of wood together. The beam is subjected to a maximum shearing force of 60kN.

1) Which of the following gives the moment of inertia at the neutral axis.

2) Which of the following gives the shearing stress at the neutral axis.

3) Which of the following gives the shearing stress at the junction between the two pieces of wood.

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 lateral buckling as follows:

1) Tensio:

F_b = 0.60F_v

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 0.60F_v

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 C_b = 1.75 + 1.05(M_1/M₂) + 0.30(M_1/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 M_1/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 C_b shall be taken as unity for cantilever beams and R₁ 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

b_f = Flange Width

t_f = 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.

F_v = 248MPa

r_t = 0.053m.

d = 0.533m.

b_f = 0.210m

t_f = 0.016m.

S_x = 0.00206m³

1) Which of the following gives the max. slenderness ratio above which is     considered long beam.

2) Which of the following gives the allowable bending stress in compression flange.

3) Which of the following gives the moment at the left end.

Solution:

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Section 5.8.3.3 of the 1992 National Structural Code of the Philippines provides the following table for approximating moments.

Positive Moment

End Spans

Discontinuous end unrestrained …………….(w_uL_n²/11)

Discontinuous end integral with support ……(w_uL_n²/14)

Interior Spans

Negative moment at exterior face of first interior support

Two Spans ………………………………………(w_uL_n²/9)

More than two spans …………………………..(w_uL_n²/10)

Negative moment at other faces of interior support ..(w_uL_n²/11)

Negative moment at face of all support for: slabs with spans not exceeding 3.00m., and beams where ratio of sum of column stiffness to beam stiffness exceeds eight at each end

of span ………………………………………………( w_uL_n²/12)

Negative moment at interior face of exterior support for members built integrally with supports

When support is spandrel beam (w_uL_n²/24)

When support is a column ……..(w_uL_n²/16)

Where L_n is the clear span

1) From the figure RC-10 shown, which of the following gives the factored uniform load?

2) Which of the following gives the factored moment at C.

3) Which of the following gives the factored moment at H.

Solution:

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The base of the footing is 1.8m. below the ground surface. It has a surcharge of 4.8kPa on the ground surface. The thickness of the footing is 1.2m. Allowable bearing pressure of the soil is 280kPa. Weight of concrete is 24kN/m³ and soil is 18kN/m³.

1) Which of the following gives the effective bearing pressure of soil.

2) Which of the following gives the distance of the resultant force from the extreme face of the column in order to have a uniform distribution of pressure.

3) Which of the following gives the dimension of the footing.

Solution:

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Allowable unit stresses in Newtons per square mm of cross-sectional area of square or rectangular simple solid columns shall be determined by the following formulas, but such unit stresses shall no exceed values for compression, parallel to grain Fc as shown in the tables adjusted in accordance with the provision of sections of 3.4 of the National Structural Code.

A timber column of square cross section has a length of 3.6m. and a dimension of 150mm x 150mm. It is fixed at both ends so that K = 0.67. The relevant code on the compressive strength Fc is given on the specifications and also a table of timber with their corresponding working stresses for visually stress-graded unseasoned Apitong with 80% stress grade.

1) Short column

a. Short column
b. Intermediate column
c. Long column
d. Not allowed by the code

2) Which of the following gives the allowable compressive stress.

3) Which of the following gives the allowable axial load.

Solution:

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For the machine part shown in the figure, the load 150 kN is acting at A.r

1) When force at A is transferred to B, what is the equivalent couple in kN.m

2) What is the force at C.

3) What is the force at B.

Solution:

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The propped beam shown has a span of 5m. EI = 1 x 10⁶ kN.m²

1) Which of the following gives the reaction at B.

2) Which of the following gives the moment at A.

3) Which of the following gives the angle of rotation at B.

Solution:

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The approved agency estimate (AAE)  of a Gov’t. project is 280M. The bids are;

Bidder A = P331,000,000

Bidder B = P337,000,000

Bidder C = P265,000,000

Bidder D = P322,000,000

Bidder E = P314,000,000

The implementing rules and regulation of P.D. Decree No. 1594 states that no award of contract shall be made ot a bidder 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 shell not be considered.

1) Which of the following gives the max. value of bid to be considered?

2) Which of the following gives the min. value of bid to be considered.

3) Which of the following are considered responsive bidders?

Solution:

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