BPSC AE Civil Paper 5 (Civil) Mock Test - 2 - Civil Engineering (CE) MCQ

Concept:

Thin spherical walls.

The hoop stress/longitudinal stress of a spherical shell is given by

The hoop strain / longitudinal strain of a spherical shell is given by

The volumetric strain is given by 3 times the hoop strain as the strain is same in all directions because sphere is same about all the axes. (Option 4)

Calculation:

Given:

P = 10 MPa; t = 25 mm; d = 500 mm; E = 20 GPa; μ = 0.3;

Now

ϵV = 3 × ϵH = 3 × 1.75 × 10-4 = 5.25 × 10-4

Due to symmetricity the strain of the sphere in all directions is same.

Concept:

Group index of a soil is given by

G.I = 0.2 a + 0.005 ac + 0.01 bd

a = It is the portion of % passing through 75 μ sieve greater than 35 but not exceeding 75 expressed as whole number in between [0-40].

b = It is the portion of % passing through 75 μ sieve greater than 15 but not exceeding 55 expressed as whole number in between [0-40].

c = It is the portion of the numerical liquid limit greater than 40 but not exceeding 60 expressed as whole number in between [0-20].

d = It is the portion of the numerical plasticity index greater than to 10 but not exceeding 30 expressed as whole number in between [0-20].

Calculation:

I_P = 10%, Liquid Limit = 40%

% Passing through 75 micron is 35%

a = 35 - 35 = 0 < 40

a = 0

b = 35 - 15 = 20

c = WL - 40

c = 40 - 40 = 0

d = IP - 10

d = 10 - 10 = 0

G.I = 0.2 a + 0.005 ac + 0.01 bd

G.I = 0.2 × 0 + 0.005 × 0 × 0 + 0.01 × 20 × 0

G.I = 0

The chart shows the relation between stress-strain in different materials.

Concept:

Generally in volumetric batching system the amount are measured in volume (m³).This method is not accurate as compared to weight batching.In weight batching method, materials are measured on the basis of weight. It is accurate method of batching.

Density of cement = 1440 kg/m³

Volume of one bag (50 kg) of cement = 0.03472 m³

Calculation:

Mix proportion given = 1 : 3 : 6

Given weight of cement = 50 kg

Volume of cement = 0.034m³

Volume of sand = 0.03472 × 3 = 0.1042 m³ = 104.2 ℓ = 105 ℓ

Given, P = 120 N at C

Free body diagram

Let R_A and R_B are the reaction at the fixed end A and B.

RA + R_B = P

Sign convetion: +ve(Tension), -ve(Compression)

As the Beam AB is fixed, So

Δ_AB = 0

Δ_AC + Δ_CB = 0

After solving,

R_B = P/3 = 120/3 = 40 N

R_A = P - R_B = 120 - 40

R_A = 80 N

As per CI. 3.1 of IS 875 (part 2), Imposed floor loads for different occupancies:

Concept:

Distribution factor (DF):

Or

Where M₁, M₂, M₃, and M₄ are moment induced in member OA, OB, OC, and OD respectively.

The summation of DF for all members at a joint is one.

Muller-Breslau Principle:

1. It states that "If an internal stress component or a reaction component is considered to act through some small distance and thereby to deflect or displace a structure. The curve of deflected structure will influence line stress or reaction component".
2. It is used to draw influence line diagrams for determinate and indeterminate structures.
3. ILD for determinate structure is linear while that for the indeterminate structure will be curvilinear.
4. This method is based on the concept that Influence lines are deflection curves.
5. It is a straight application of Maxwell's reciprocal theorem.
6. ILD is a graphical representation of variation in the reactions, Shear force, and bending moment at each and every section when unit load moves from one to another end of the structure. They can be drawn for any type of structure – beams, arches, trusses, etc.

For example, to draw the influence line diagram for a vertical reaction at A in a simply supported beam as shown below.

Remove the ability to resist movement in the vertical direction at A by using the guided roller

BIS stipulations for use of flyash in concrete:

As per clause 5.2 of IS 456-2000 Plain and Reinforced cement concrete code of practice,

1) Flyash (conforming to IS: 3812 Part–1) up to 35% can be used as part replacement of OPC in the concrete.

2) As per the note of table 5 of this code of practice, addition of flyash quantity can be taken into account in the concrete composition with respect to cement content and water cement ratio.

The characteristics of under-reinforced section and over a reinforced section when compared with balanced section are given below in the tabulated form.

So, For an under-reinforced beam, steel yield prior to concrete failure. Stresses in steel reach permissible value whereas stress in concrete has not reached up to its permissible value.

σ_s = f_y and σ_c < f_c

Concept:

Taylor's stability number method:

(i) Taylor introduced a dimensional parameter, called Taylor's stability number, which is given by

Where, H = Effective height of slope

Hc = Critical height of slope

F = FOS

(ii) In this method, Taylor's stability number is read from Taylor's chart in order to analyze the stability of slope for a given value of strength parameters of the soil.

(iii) Taylor's method is suitable for c-ϕ soils and for ϕ = 0 (pue clays)

Calculation:

Given, C = 30 kN/m2, γ = 25 kN/m³ and S_n = 0.05, F = 1

∵ We know that,

⇒

H_c = 24 m

The cement of the desired color may be obtained by intimately mixing mineral pigments with ordinary cement. The amount of coloring material may vary from 5% to 10%. If the percentage exceeds 10%, the strength of the cement is affected.

The list of pigments used in cement and their corresponding colure obtained is given below in the tabulated form:

Note:

1. The chloride does not impact the color of cement and it will produce the cement of its natural color i.e., grey. There is an error in question.
2. Iron Oxide pigments are one of the most used pigments. These pigments protect the concrete/cement from fading or prevent the leaching out of concrete/cement.

The fineness of the cement is checked to test the proper grinding of the cement which significantly influences the rate of hydration. These two methods are used for the determination of the fineness of cement:

1) Air permeability method ( Blaine)

The fineness of cement is measured as the specific surface.

Specific surface is expressed as

• The total surface area in square meters of all the cement particles in one kilogram of cement or
• The total surface area in square cm per gram of cement.

The higher the specific surface is, the finer cement will be.

Fineness test is performed on the Blaine apparatus. It is practically a manometer in the U-tube form. One arm of the manometer is provided at the top with a conical socket to form an airtight fit with the conical surface of the cell.

2) Sieving method

• This method serves only to demonstrate the presence of coarse cement particles. This method is primarily suited to checking and controlling the production process. The fineness of cement is measured by sieving it on standard sieves. The proportion of cement of which the grain sizes are larger than the specified mesh size is thus determined.

Additional Information

• The soundness of cement may be determined by two methods, namely the Le-Chatelier method, and the autoclave method.
• The Vicat Apparatus: It is used to measure the setting time and consistency of concrete.

Solution:

The θ_A and θ_B can be calculated using conzugate beam method.

In this method,

Rotation at any point in real beam = shear force at that point in conzugate beam

Deflection at any point in Real beam = Bending moment at that point in conzugate Beam

Also, the loading on conzugate beam is the diagram of real beam.

Calculation:

Congugate Beam:

∴ (clockwise)

Now, ∑F_y = 0

θ_A : θ_B = 1 : 2

Shear span

• It is the span between the points of application of concentrated load to its adjacent Reaction force in a beam.
• If a simply–supported beam of span L carries a moment force at its mid-span, then the shear force diagram will be rectangular, and the bending moment diagram will be triangular.

Shear span is defined as the zone where shear force is constant.

Note:

• Throughout Shear Span the Shear Force is constant.
• There might be multiple shear spans for a single beam depending upon the number and position of applied force to the numbers of supports.

• Corrugated steel sheets 14%
• Corrugated asbestos cement sheets 20%
• Semi–corrugated asbestos cement sheets 10%
• Nainital pattern roofs ( plain sheeting with rolls ) 10%
• Nainital pattern roofs with corrugated sheets 25%

Additional Information

1. Cornices and other wall features, when not picked out in a different finish/colour, shall be girthed and included in the general area.

2. The painting for building surfaces shall be kept separate and the surfaces to be painted shall be described. It shall be stated whether measurements are flat or girthed. Alternatively. different surfaces may be grouped into one general item, areas of uneven surfaces are converted into equivalent plain areas by increasing the areas as under:

• External walls of plain brickwork faced with recessed, raised or weather stuck pointing-20 percent
• Sand face plaster with up to 4 mm Size 50 percent
• Roughcast plaster with stone aggregate up to 10 mm-IOO percent
• Pebbledash finish beyond 10 mm-275 percent
• Sponge finished plaster-25 percent

Concept:

1) Single shear case:

• The shear force P in the shear plane is equal to tension force F.
• The average shear stress in the plane is .
• This joint is said to be in single shear.

2) Double shear case:

• If the plates, which are connected by a rivet as shown in the following figure, are subjected to tension forces, shear stresses will develop in the rivet.
• This joint is said to be in double shear.
• Observing that the shear P in each of the planes is , the average shearing stress is

Calculation:

Given:

Force, F = 12 kN, Area, A = 115 mm²

Single shear stress-induced = τ_avg

τ_avg = 104.34 N/mm²

∴ The average shear stress, in this case, is 104.34 N/mm²

Concept:

Development length:

(i) The calculated tension or compression in any bar at any section shall be developed on each side of the section by an appropriate development length or end anchorage or a combination thereof.

(ii) Development length can be calculated as:

Where, ϕ = Diameter of bar

τbd = Design bond stress = Permissible value of average bond stress

The value of bond stress is increased by 60% for a deformed bar in tension and a further increase of 25% is made for bars in compression.

Calculation:

Given,

ϕ = 20 mm, τbd = 1.4 N/mm2 (In tension), f_y = 415 MPa

∵ Bar in compression, so Increased the value of τbd by 25% and for deformed bar it is increased by 60 %

So, τbd = 1.4 × 1.25 × 1.6 = 2.8 N/mm2

Development length,

= 645 mm

Modular Ratio:

(i) In case of working stress method of analysis, the composite section of reinforced concrete is transformed into an equivalent section of single material of concrete. for this, we need to define modular ratio which is the ratio of elastic modulus of steel to concrete.

(ii) However, the short term modulus of elasticity of concrete does not take into account the long term effects of creep and shrinkage and thus it is not considered in defining the modular ratio (m). However, partly taking into account the long term effects of creep and shrinkage, CI. B-1.3 of IS 456:2000 defines modular ratio (m) as:

Where, σ_cbc = Permissible stress n concrete in bending compression

As per IS code:

An additional saving of 15 to 30 percent is possible in concrete due to the use of concrete in the tension zone, compared to reinforced concrete high tensile steels used in prestressed members and its ultimate strength is equal to 2100 N/mm² and the savings include steel and is even higher, 60 to 80 percent mainly due to higher permissible stresses permissible in high tension wires.

Operations involved in manufacturing of clay brick are:

Preparation of brick earth

1. Unsoiling

The soil used for making building bricks should be processed so as to be free of gravel, coarse sand (practical size more than 2 mm), lime and kankar particles, organic matter, etc. About 20 cm of the top layer of the earth, normally containing stones, pebbles, gravel, roots, etc., is removed after clearing the trees and vegetation.

2. Digging

After removing the top layer of the earth, proportions of additives such as fly ash, sandy loam, rice husk ash, stone dust, etc. should be spread over the plane ground surface on a volume basis. The soil mass is then manually excavated, puddled, watered and leftover for weathering and subsequent processing.

3. Weathering

The soil is left in heaps and exposed to the weather for at least one month in cases where such weathering is considered necessary for the soil. This is done to develop homogeneity in the mass of soil, particularly if they are from different sources, and also to eliminate the impurities which get oxidized. The plasticity and strength of the clay are improved by exposing the clay to weather.

4. Blending

The earth is then mixed with sandy-earth and calcareous-earth in suitable proportions to modify the composition of the soil. A moderate amount of water is mixed so as to obtain the right consistency for moulding.

5. Tempering

It is done in pug mill and the process is called pugging. Tempering consists of kneading the earth with feet so as to make the mass stiff and plastics (by plasticity, we mean the property which wet clay has of being permanently deformed without cracking). It should preferably be carried out by storing the soil in a cool place in layers of about 30 cm thickness for not less than 36 hours.

6. Moulding

It is a process of giving a required shape to the brick from the prepared brick earth. Moulding may be carried out by hand or by machines.

7. Drying

The object of drying is to remove the moisture to control the shrinkage and save fuel and time during burning.

8. Burning

The burning of clay may be divided into three main stages: Dehydration stage (400 - 650°C), Oxidation period (650 - 900°C), vitrification. Burning of bricks is done either in clamps or kilns.

Concept:

Bulking of sand:

Bulking in sand Occurs When dry sand interacts with atmospheric moisture. The presence of moisture content forms a thin layer around sand particles. This layer generates the force which makes particles move aside from each other. This results in an increase in the volume of sand.

Percentage of bulking can be determined by:

Percentage of bulking of sand =

Where

h1 = Height of the sand sample

h2 = Height of the sand in water or saturated sand

Calculation:

Given,

h1 = 210 mm and h2 = 150 mm

Percentage of bulking of sand =

Percentage of bulking of sand =

Percentage of bulking of sand = 40 %.

English bond

• In this bond, the alternate courses consist of headers and stretchers.
• This is considered to be the strongest bond, So this bond is provided in brick masonry for carrying heavy loads.
• Hence it is a commonly used bond for walls of all thicknesses.

Flemish Bond

• In this type of bond, each course comprises of alternate header and stretcher.
• Alternate courses start with stretcher and header.
• Every header is centrally supported on the stretcher below it.
• Construction of Flemish bond needs greater skill.
• Used to get a good aesthetic view.

Important Point

To break the continuity of vertical joints

• In English bond - Queen closer is used in the beginning and end of a wall after the first header.
• In Flemish bond - Queen closers are required if a course starts with a header and in walls having their thickness equal to odd number of half bricks, bats are essentially used to achieve the bond.
• In Header bond - 3/4 brick bat as a quoin brick in alternating courses.
• Stretcher bond - 1/2 brick bat is provided in alternating courses.

Concepts:

The strain energy is the energy stored in a body due to its elastic deformation.

The most general formula for strain energy is:

Where, F is the applied force and δ is deformation

However, When stress

; V is the volume of material.

Based on the above formals, the strain energy stored in the material due to different types of forces/moments is given as:

1. Strain energy due to bending is:

2. Strain energy due to Torsion is :

Concept:

Conjugate beam method:

Conjugate beam is defined as a imaginary beam with the same dimension as that of original beam but load at any point on the conjugate beam is equal to bending moment at that point divided by EI (Flexural Rigidity).

Conjugate beam can be made by changing the supports

Note: The shear force in conjugate beam at a point is slope at the point in real beam. The bending moment in conjugate beam at a point is the deflection at the point in real beam.

Shear strength of the soil:

The shear strength of a soil is its maximum resistance to shear stresses just before the failure. The shear strength (S) of soil at a point on a particular plane was expressed by coulomb as a linear function of the normal stress on the plane as,

S = C + σ tan ϕ

Where,

σ = Normal stress on the plane, C = Cohesion of the soil

ϕ = Angle of internal friction or angle of shearing resistance

The C and ϕ values for different soils are given below

Hence the value of the angle of internal friction is least for clays (Purely Cohesive), i.e ϕ = 0

Degree of kinematic indeterminacy, D_K= 1

So size of [K] = [1×1]

Calculation:

θ_AB = 45°

Example:

Vertical Stiffeners:

• Vertical stiffeners are provided to prevent buckling of the web due to diagonal compression.

Some criteria regarding the design of vertical stiffness:

• The spacing between the vertical stiffness should be between 0.33 × d and 1.5 × d, d is the distance between flange angles,s, and where there is no flange angle, the distance between flanges ignoring fillets is taken.
• The greater unsupported clear dimension of the web panel should not be greater than 270 times the thickness of the web and the lesser unsupported clear dimension of the same web panel should not be greater than 180 times the thickness of the web.
• The length of the outstanding leg of vertical stiffness may be taken equal to 1/30 of the clear depth of girder plus 50 mm and the outstanding of stiffener from web shall not be more than , where t is the thickness of the section )
• The length of the connected leg of vertical stiffness should be sufficient to accommodate the rivets connecting the stiffness to the web. The amount of moment `of inertia I of the stiffness selected should not be less than

I <

Where I is the moment of inertia of pair of stiffness about the center of the web

t_w = Minimum required thickness of the web

C = Maximum permitted distance between the vertical stiffeners

Dry rot:

(i) The fungi of certain types feed on wood and during feeding, they attack on wood and convert it into powder form. This is known as the dry rot.

(ii) The dry rot occurs at places where there is no free circulation of air such as improperly ventilated basements, rooms, etc., and in damp situations like kitchen, toilets, etc.

(iii) The unseasoned softwood and sap wood are easily attacked by dry rot.

(iv) The most favorable conditions for the rapid growth of the fungus responsible for dry rot are the absence of sunlight, dampness, presence of sap, stagnant air, and warmth.

(v) When part of timber is seriously affected by dry rot, the damaged portion may be completely removed and the remaining unaffected portion should be painted with a solution of copper sulphate.

Solignum paint:

• These paints preserve the timber from white ants as they are highly toxic in nature. They can be mixed with colour pigments and applied in hot state with the help of brush.

Coal tar:

• In this method, timber section is applied with hot coal tar that increases its resistance against the penetration of water and fire.
• Coal tar gives an unpleasant smell and appearance hence it is generally used for works of minor importance
• The process of application of coal tar over timber surface is referred to as tarring.

Creosote:

• In this case, the timber surface is coated with creosote oil. The process is known as the creosoting or Bethel's process of preservation of timber.
• The creosote oil is obtained by the distillation of tar.
• It is observed to have the best antiseptic properties there by is highly affected in killing fungi, insects and termite.