Civil Engineering Online Review

A concurrent force system in space is composed of 3 forces described as follows P₁ has a magnitude of 100kN and acts through the origin and points x =3, y =4, z=2. P₂ has a magnitude of 60kN and acts through the origin and points x = 4, y = 1, z = -2. P₃ has a magnitude of 80kN and acts through the origin and points x = 2, y = -3, z = 3.

1) Which of the following most nearly gives the x-component of the resultant force.

2) Which of the following most nearly gives the y-component of the resultant force.

3) Which of the following most nearly gives the z-component of the resultant force.

Solution:

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For continuous beams and slabs, approximate coefficients of shear and bending moments in accordance with the NSCP Specifications may be utilized when the following conditions are satisfied.

1) Adjacent clear spans may not differ by more than 20% of the shorter span.

2) Ratio of live load to dead should be less than 3.

3) The loads must be uniformly distributed.

When all conditions are satisfied, the following formulas maybe used to determine shear forces and bending moments in continuous beam and one way slabs.

A) For positive moment

End span:

1) If discontinuous ends is unrestrained

………        (WL’²/11)

2) If discontinuous ends is integral with the support

………        (wL’²/14)

3) Interior spans

………        (wL’²/16)

B) For negative moment

1) Negative moment at exterior face of first interior support.

Two spans ………        -(wL’²/9)

More than two spans ……… -(wL’²/10)

2) Negative moment at other faces of interior supports

………        (wL’²/11)

3) Negative moment at face of all supports for

a) Slabs with spans not exceeding

3m    ………        -(wL’²/12)

b) Beams and girders when the ratio of sum of column stiffness to beam stiffness exceeds 8 at each

end of the span    ………       -(wL’²/12)

3) Negative moment at interior faces of exterior supports, for members built integral with their supports.

a. Where the support is a spandrel beam or girder

………    -(wL’²/24)

b. Where the support is a column

………    -(wL’²/16)

C) Shear Forces:

1) Shear in end members at first interior support ……… (1.15wL’/2)

2) Shear at the other support ……. (wL’/2)

The figure shown is a continuous beam having given clear spans of L₁ = 6m., L₂ = 7m and L₃ = 8m. It carries a uniform dead load of 12 kN/m and a uniform dead load of 12kN/m and a uniform live load of 30 kN/m. It is required to compute the following. Use NSCP moment coefficients.

1) Which of the following most nearly gives the moment at A.

2) Which of the following most nearly gives the moment at B.

3) Which of the following most nearly gives the moment at C.

Solution:

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A bill of quantities is to be prepared for square isolated reinforced concrete column and footing as shown. The foundation is strong enough that form works is not required for footing. The swell factor for backfill is 120%.

1) Which of the following most nearly gives the quantity of excavation in m³.

2) Which of the following most nearly gives the quantities of form works is sq.m.

Solution:

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Section 4.5.1.3.1 of the NSCP specifies the allowable axial compressive members whose cross-sections meet with the provisions of the code.

A compression member is 3m. long and pinne at both ends. Effective length of factor K = 1.0. The column is subjected to an axial compressive load of 590kN. The section is made up of 2 angles of unequal legs with long legs back to back and separated by a gusset plate 11mm thick. Use A 36 steel, Fy = 248 MPa and E = 200000 MPa.

1) Which of the following gives the largest allowable compressive stress.

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

3) Which of the following gives the most economical setion.

Section	Area(m2)	rx(m)	ry(m)
2- < 120×80x10	0.0056	0.040	0.018
2- < 1150×90x12	0.0062	0.052	0.021
2- < 180×100x10	0.0079	0.060	0.026

Solution:

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A rectangular reinforced concrete beam with width of 300mm and effective depth of 600mm is subjected to a service (unfactored) bending moment  of 200kN.m. The beam is reinforced with 4-32mmØ bars. The modular ratio n = 8.

1) Using the alternate (working stress) Design method. Which of the following most nearly gives the distance of the neutral axis from the top of the beam (kb) in mm.

2) Which of the following most nearly gives the maximum stress in concrete in MPa.

3) Which of the following most nearly gives the total comp. force in concrete in kN.

Solution:

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A W 16 x 58 is connected to W 18 x 31. Use A-36 steel Fy = 248MPa. Allowable stress S_s = 0.40 Fy. A 502 grade hot driven rivets with an allowable shearing stress of 120MPa and allowable bearing stress of 1.5 Fu(AISC). The support is to be designed using the full strength of W 16 x 58 beam based on the gross section.

Properties of sections

W 16 x 58             W 18 x 31

d = 403mm          Flange thickness = 11mm

Web thickness = 10mm

1) Which of the following most nearly gives the minimum diameter of rivets not the exceed allowable shear stress.

2) Which of the following most nearly gives the minimum diameter of rivets not to exceed allowable bearing stress.

3) Which of the following most nearly gives the minimum diameter of rivets.

Solution:

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A truss shown in the figure is subjected to a horizontal force at joint C. The term E below refers to the modulus of elasticity of the material in Pa and the term A refers to the cross-sectional area of the members. The truss is to be analyzed using the method of superposition.

1) Which of the following most nearly gives the relative displacement of joint B and D, if member BD is removed in meters.

2) Which of the following most nearly gives the relative displacement of joint B and D due to two unit loads (N) acting at joint B and D acting towards each other in the direction of member BD, if the member BD is removed in m.

3) Which of the following most nearly gives the value of the bar force in member BD in Newtons.

Solution:

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From the beam shown in the figure.

1) Which of the following gives the fixed end moment at B due to the concentrated load in kN.m.

2) Which of the following most nearly gives the distribution factor at B for the member AB in %

3) Which of the following most nearly gives the moment at B.

Solution:

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Three identical cylinders are stacked within a rigid bin as shown in the figure weight of each cylinder is 500 N. There is no friction at any contact surface.

1) Which of the following most nearly gives the force at A, in Newtons.

2) Which of the following most nearly gives the force at B, in Newtons.

3) Which of the following most nearly gives the force at C, in Newtons.

Solution:

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A piece of equipment was purchased for P4,000,000.00 The useful life is estimated at 5years with no salvage value. The equipment is estimated to be used 1000 hours every year Operating costs are as follows:

Fuel ………….10 liters/hour @ P10 per liter

Oil ……………1 liter/hour @ P20 per liter

Grease ……….2 liters/hour @ P5 per liter

The equipments uses 6 tires costing P60,000 each. Estimated life of tires is 4000 cost of money is 15% per year. Cost of insurance taxes, storage, etc. is 15% per year.

1) Which of the following gives the cost of using the equipment only in pesos per hour.

2) Which of the following gives the cost of using the tires in pesos per hour.

3) Which of the following gives the cost of using the equipment and tires in pesos per hour.

Solution:

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For the forces in the figure shown

1) Which of the following most nearly gives the magnitude of the horizontal component of the resultant of the force system?

2) Which of the following most nearly gives the magnitude of the resultant force?

3) Which of the following gives the angle that the equilibrant makes with the horizontal axis.

Solution:

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1) For the wall footing shown in the figure, which of the following most nearly gives the effective soil pressure if the allowable soil pressure is 200kPa. (the effective soil pressure is the remaining soil pressure available to support the loads after the effects of the soil an concrete weights are subtracted) fc’ = 28 MPa fy = 280MPa

Unit weight of concrete = 24kN/m³

Unit weight of soil = 16kN/m³

Allowable soil pressure = 200kPa

P_D = 200kN/m

P_L = 180kN/m

2) Which of the following most nearly gives the minimum width of footing rounded to the nearest 0.10m. such that the effective soil pressure will not be exceeded.

3) Which of the following most nearly gives the ultimate shear due to factored loads acting or, the critical section.

Solution:

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Given the beam shown in the figure, in equation (1) and (2) below, the terms are as follows:

A_xy = area of the moment diagram of the given load acting on a simple beam

X_xy = distance of centroid of A_xy from point x

I = moment of inertia of member

L_xy = span length of member xy

1) Determine the value of the expression:

Representing the contribution of the uniform load and concentrated load acting on the span ab, to the three-moment equations of two-span beam.

2) Determine the value of the expression:

Representing the contribution of the triangular load acting on the triangular load acting on the span bc, to the three-moment equations of two-span beam.

3) Compute the maximum negative moment.

Solution:

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A sand layer of the cross-sectional area shown in the figure below has been determined to exist for a 450m. length of levee. The coefficient of permeability of the sand layer is 3m per day. Compute the quantity of water which flows into the ditch.

Solution:

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A plate with width of 300mm and thickness of 20mm is to be connected to two plates of the same material with half the thickness, by 25mm diameter rivets, as shown in the figure. The rivet holes have a diameter 2mm larger than the rivet diameter. The plate is A36 steel with yield strength Fy = 248 megaPascals, allowable tensile stress of 1.35 Fy. The rivets are A502, Grade 2, hot-driven rivets with allowable shear stress of 150 megaPascals.

1) Which of the following most nearly gives the max. load in kN that can be applied to the connection without exceeding the allowable shear stress in rivets.

2) Which of the following most nearly gives the max. load in kN that can be applied to the connection without exceeding the allowable bearing stress between the plates and the rivets.

3) Which of the following most nearly gives the max. load in kN that can be applied to the connection without exceeding the allowable tensile strength of the plates.

Solution:

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For the shaded area a given in the figure.

1) Determine the area, in square meters.

2) Determine the x-coordinate of the centroid, in meters.

3) Determine the y-coordinate of the centroid, in meters.

Solution:

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1) Determine the reinforcement ratio, in percent

2) Determine the ratio of the center spacing of reinforcement to the column dimension in the direction of bending.

3) Using the interaction Diagram, determine the maximum downward load that the column can support, in kN, if eccentricity e = 200mm.

Solution:

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A simply supported beam with span of 8meters is subjected to a uniform vertical downward load equal to 50kilo Newtons/meters, acting on the plane of the minor axis of the beam section, which includes the beam weight. The beam is restrained against lateral buck.ing of the top and bottom flanges for the entire span. The material is A36 steel with f_y = 248 megaPascals and modulus of elasticity = 200 gigaPascals. The allowable flexural stress for laterally braced compact sections is 0.66 f_v. The allowable deflection is 1/360 of the span. Three compact sections are being considered, as follows, with their respective properties relevant to this problem (length units are in meters):

	Section	Moment of Inertia	Beam Depth
1	W 24 x55	0.000558 m4	0.598m.
2	W 21 x 62	0.000554 m4	0.533m.
3	W 21 x 68	0.000616 m4	0.537m.

1) Determine the minimum section modulus S_x, in m³, such that the maximum flexural stress will not be exceeded.

2) Determine the minimum moment of inertia I_x, in m⁴, such that the maximum deflection will not be exceeded.

3) Assuming that shear stress is not critical, which of the sections being considered is the most economical section adequate for the given load.

Solution:

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A simply-supported beam has shear diagram shown in the figure.

1) Determine the maximum positive bending moment, n kN-m.

2) Determine the maximum negative bending moment, in kN-m

3) Determine the location of the inflection point from the support, in meters.

Solution:

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The result of a grading analysis is the particular size distribution shown in the figure. Determine the effective grain size D₁₀.

a) 0.10

b) 0.07

c) 0.09

d) 0.08

Solution:

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A soil sample is placed in a brass box. The soil is gripped by perforated metal grilles and porous discs are behind the metal grilles to allow the sample by means of a 500kg weight and while applying the normal load, a lateral force is gradually exerted in the box using an electrical screw jack. The force and the corresponding cross section of specimen are recorded during the test. This is known as:

a) Consolidated drain test

b) Direct shear test

c) Undrained shear test

d) Unconfined compression test

Answer:

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