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Question 1
ప్రశ్న 1
Which loading condition best represents an RCC column subjected to combined axial compression and uniaxial bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Uniaxial bending means that the significant bending action is considered about one axis of the column section. The member simultaneously carries an axial compressive force. The stress and strain distribution is therefore different from both pure axial compression and pure bending. Section capacity has to satisfy the combined effects of Pu and Mu. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
A factored axial compressive load of 1500 kN acts on a column with an eccentricity of 100 mm about one axis. What uniaxial bending moment accompanies the axial load?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For an axial force acting at an eccentricity, the corresponding moment is M = Pe. The eccentricity of 100 mm is 0.10 m. Hence M = 1500 × 0.10 = 150 kN·m. This moment acts together with the axial compression and cannot be treated independently of it when checking the column section. Therefore Option C is correct.
వివరణ:
Question 3
ప్రశ్న 3
A column analysis gives a factored axial load Pu = 2000 kN and a factored uniaxial moment Mu = 160 kN·m. What is the corresponding resultant eccentricity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The eccentricity corresponding to a combined axial force and moment is e = Mu/Pu. Here e = 160/2000 = 0.08 m. Converting to millimetres gives 80 mm. This calculated eccentricity can then be compared with the code-prescribed minimum eccentricity where relevant. Therefore Option B is correct.
వివరణ:
Question 4
ప్రశ్న 4
For a column direction having unsupported length 3.60 m and lateral dimension 450 mm, the code minimum eccentricity is 22.2 mm. Structural analysis gives an eccentricity of 70 mm in the same direction. Which eccentricity should govern the combined axial-load and bending design?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The code minimum eccentricity is intended to prevent design for unrealistically perfect concentric compression. Where the calculated eccentricity from structural analysis is larger, that calculated eccentricity governs. The minimum eccentricity is not added to the larger calculated eccentricity. Here 70 mm exceeds 22.2 mm, so the design should use the effects corresponding to 70 mm. Therefore Option C is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which statement correctly describes the IS 456 approach to a column subjected to axial force and uniaxial bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
IS 456 Clause 39.5 deals specifically with members subjected to combined axial load and uniaxial bending. The section has to be assessed using the relevant compression-member assumptions together with the minimum-eccentricity requirement. Axial resistance and flexural resistance are coupled through compatibility and equilibrium. Consequently, a satisfactory axial-only check does not by itself establish adequacy under combined loading. Therefore Option B is correct.
వివరణ:
Question 6
ప్రశ్న 6
Why are interaction diagrams particularly useful for the Limit State design of RCC columns under axial compression and uniaxial bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Combined axial compression and bending produces a strain distribution that depends on the neutral-axis position. For each trial condition, concrete and reinforcement forces must satisfy both force and moment equilibrium. Repeating this process directly can involve substantial trial-and-error calculation. Interaction diagrams present the resulting capacity combinations in a convenient graphical form. Therefore Option C is correct.
వివరణ:
Question 7
ప్రశ్న 7
In a Pu-Mu interaction diagram for a given RCC column section and reinforcement arrangement, what does a point on the ultimate interaction boundary represent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
An interaction boundary represents combinations of axial force and bending moment that bring the section to its ultimate design capacity under the adopted assumptions. Different locations on the boundary correspond to different neutral-axis positions and strain states. The diagram therefore does not represent only one fixed eccentricity. A demand combination must lie within the section's available combined strength rather than beyond the capacity boundary. Therefore Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
Which pair of dimensionless parameters is commonly used on SP 16 interaction charts for a rectangular column of breadth b and overall depth D?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Dimensionless parameters make the interaction charts applicable to sections of different absolute sizes within their stated assumptions. For rectangular columns, the normalized axial-load parameter is Pu/(fck bD). The corresponding normalized moment parameter is Mu/(fck bD²). Other parameters identify reinforcement percentage, steel grade, cover ratio and reinforcement arrangement. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
An M25 rectangular column has b = 400 mm and D = 500 mm and carries Pu = 1800 kN. What is the normalized axial-load parameter Pu/(fck bD)?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The denominator is fck bD = 25 × 400 × 500 = 5,000,000 N. The factored axial load is 1800 kN = 1,800,000 N. Therefore Pu/(fck bD) = 1,800,000/5,000,000 = 0.36. This dimensionless ordinate can be used with an appropriate interaction chart. Therefore Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
For the same M25 column with b = 400 mm and D = 500 mm, a factored moment Mu = 175 kN·m acts about the axis for which D = 500 mm. What is Mu/(fck bD²)?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The moment must first be expressed in N·mm, giving 175 × 10^6 N·mm. The denominator is 25 × 400 × 500² = 2.5 × 10^9 N·mm. The normalized moment is therefore 175 × 10^6 divided by 2.5 × 10^9. This equals 0.070. Therefore Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
For a 400 mm × 500 mm column containing 2010 mm² of longitudinal steel, what is the longitudinal steel percentage p based on the gross area bD?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The gross cross-sectional area is 400 × 500 = 200000 mm². The steel percentage is p = 100Asc/(bD). Substitution gives p = 100 × 2010/200000 = 1.005 percent. This percentage is one of the quantities used in selecting or interpreting column interaction curves. Therefore Option B is correct.
వివరణ:
Question 12
ప్రశ్న 12
If the column in the previous question uses M25 concrete, what is the value of the interaction-chart parameter p/fck approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The reinforcement percentage is approximately 1.005. The characteristic concrete strength is fck = 25 N/mm². Thus p/fck = 1.005/25 = approximately 0.0402. This is normally represented by the nearest appropriate family of reinforcement curves or by interpolation where applicable. Therefore Option B is correct.
వివరణ:
Question 13
ప్రశ్న 13
A rectangular column has overall depth D = 500 mm and the centroid of the outer longitudinal reinforcement is 50 mm from the highly compressed face. What cover ratio d'/D is used for interaction-chart selection?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The interaction-chart cover parameter is based on the distance d' from the extreme face to the centroid of the relevant reinforcement. Here d' = 50 mm and D = 500 mm. The ratio is therefore d'/D = 50/500 = 0.10. A chart corresponding to the appropriate cover ratio and steel arrangement is then selected. Therefore Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
Which set of information is particularly important when selecting an appropriate SP 16 interaction chart for a rectangular RCC column under uniaxial bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Interaction charts are based on specified material and reinforcement configurations. The grade of reinforcing steel affects the steel stress-strain response. The d'/D ratio influences the lever arms and strains in the reinforcement. Whether reinforcement is distributed on two opposite faces or on all four faces also changes the section response. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
For a selected SP 16 interaction chart, which parameter is commonly used to identify the appropriate reinforcement curve within the family of curves?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Once the applicable chart is selected for the steel grade, cover ratio and reinforcement pattern, a family of curves is available. These curves are commonly identified using the reinforcement parameter p/fck. Here p is the percentage of longitudinal reinforcement based on the gross rectangular section. The design load and moment parameters are then located relative to the appropriate curve. Therefore Option A is correct.
వివరణ:
Question 16
ప్రశ్న 16
For an M25 column with b = 400 mm and D = 500 mm, an appropriate interaction chart gives a normalized moment capacity Mu/(fck bD²) = 0.08 at the specified axial load. What uniaxial design moment capacity does this represent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The dimensional moment capacity is obtained by multiplying the normalized value by fck bD². Here fck bD² = 25 × 400 × 500² = 2.5 × 10^9 N·mm. Multiplying by 0.08 gives 200 × 10^6 N·mm. This is 200 kN·m. Therefore Option C is correct.
వివరణ:
Question 17
ప్రశ్న 17
At a specified factored axial load, an interaction chart indicates a uniaxial moment capacity of 200 kN·m. The design action is 180 kN·m at that same axial load. Which strength conclusion follows, considering only the Pu-Mu interaction check?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The chart capacity must be evaluated at the same factored axial load as the design demand. At that axial load, the section can resist up to the stated 200 kN·m moment. The required moment is only 180 kN·m. Thus the combined strength demand does not exceed the stated uniaxial capacity for this check. Therefore Option B is correct.
వివరణ:
Question 18
ప్రశ్న 18
At a specified axial load, an interaction chart gives a moment capacity of 190 kN·m, while the factored design moment is 220 kN·m. What should be concluded?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The available moment capacity must not be less than the required factored moment at the specified axial load. Here the capacity is 190 kN·m but the demand is 220 kN·m. The combined load point therefore exceeds the stated sectional capacity. A larger section, different reinforcement, higher material strength or another appropriate design change would be necessary. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
For a fixed axial load Pu = 1800 kN, increasing the load eccentricity from 50 mm to 75 mm changes the primary first-order moment from 90 kN·m to what value?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The moment associated with an eccentric axial load is M = Pe. For e = 75 mm, the eccentricity in metres is 0.075 m. Hence M = 1800 × 0.075 = 135 kN·m. Increasing eccentricity at the same axial force therefore directly increases the first-order bending demand. Therefore Option C is correct.
వివరణ:
Question 20
ప్రశ్న 20
Under the IS 456 Limit State assumptions, which statement is correct regarding concrete tension in determining the ultimate strength of a column section under combined axial compression and bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Limit State sectional assumptions used for reinforced concrete flexure and compression do not rely on concrete tensile strength. Once a part of the section is in tension, the tensile concrete contribution is ignored in the ultimate strength calculation. Tensile force needed for equilibrium is primarily provided by reinforcement. This assumption is important when eccentricity is large enough to produce tension on one side of the section. Therefore Option B is correct.
వివరణ:
Question 21
ప్రశ్న 21
For an RCC section under axial compression combined with bending and with no tension over the section, IS 456 relates the maximum compressive strain at the highly compressed extreme fibre to the strain at the least compressed extreme fibre. If the least compressed extreme-fibre strain is 0.0010, what maximum strain is permitted at the highly compressed extreme fibre?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For axial compression with bending and no tension on the section, the relevant strain relation is 0.0035 minus 0.75 times the strain at the least compressed extreme fibre. Substituting 0.0010 gives 0.0035 - 0.00075. The result is 0.00275. This relation connects the axial-compression strain state with the bending-dominated strain state. Therefore Option C is correct.
వివరణ:
Question 22
ప్రశ్న 22
How does the IS 456 strain relation for an entirely compressed section recover the pure axial-compression strain of 0.002 when both extreme fibres have the same strain?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In pure axial compression, the strain distribution is uniform over the section. Therefore the most compressed and least compressed extreme fibres have the same strain ε. Substituting this condition into the combined compression-bending relation gives ε = 0.0035 - 0.75ε. Solving gives 1.75ε = 0.0035 and hence ε = 0.002. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
During a trial-and-error analysis of an RCC column section under Pu and Mu, a selected neutral-axis position gives an internal axial resultant exactly equal to Pu but an internal resisting moment smaller than Mu. Is that neutral-axis trial acceptable as the ultimate solution?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A section under combined axial load and bending must simultaneously satisfy equilibrium of axial forces and moments. Matching only the axial resultant is not sufficient. The assumed strain profile and neutral-axis position must also produce the required resisting moment. If the internal moment is smaller than the applied Mu, another trial or a revised section is necessary. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which statement best describes the shape and meaning of an RCC column Pu-Mu interaction relationship?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The forces in concrete and reinforcement depend nonlinearly on the strain state of the section. As the neutral axis changes, different reinforcement layers may be in compression, low tension or substantial tension. The concrete compression block also changes in magnitude and position. The resulting combinations of Pu and Mu therefore form a nonlinear interaction relationship rather than a universal straight line. Therefore Option B is correct.
వివరణ:
Question 25
ప్రశ్న 25
What limiting condition is represented by the point on a Pu-Mu interaction diagram where the bending moment is zero and the axial compressive force is at its maximum section capacity for that reinforcement arrangement?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At zero moment, the resultant compressive load acts without a flexural demand about the considered centroidal axis. The corresponding interaction-diagram endpoint represents the maximum axial compression capacity under the applicable section assumptions. Moving away from that endpoint introduces bending and an eccentric strain distribution. This endpoint is therefore associated with the purely axial or concentric compression condition. Therefore Option C is correct.
వివరణ:
Question 26
ప్రశ్న 26
At the interaction-diagram condition Pu = 0 but Mu is finite, what sectional behaviour does the point principally represent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
If the resultant axial force is zero, there is no net compression or tension force acting through the section. A finite moment can nevertheless be resisted by an internal compression-tension couple. This corresponds to the pure-flexural end of the axial-force–moment interaction relationship. The reinforcement and concrete still develop internal forces even though their resultant axial force balances to zero. Therefore Option A is correct.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: A. An axial compressive force together with bending moment about one principal axis సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: C. 150 kN·m సమాధానం: C.
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Question 3 ప్రశ్న 3Answer: B. 80 mm సమాధానం: B.
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Question 4 ప్రశ్న 4Answer: C. 70 mm సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: B. The member is designed using the compression-member assumptions and minimum-eccentricity provisions, with combined force and moment equilibrium సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: C. They represent compatible combinations of axial-load and moment capacity that otherwise require iterative calculations సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: B. A combination of design axial load and design moment corresponding to the section's limit-state capacity సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: A. Pu/(fck bD) and Mu/(fck bD²) సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: C. 0.36 సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: B. 0.070 సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: B. 1.005 percent సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: B. 0.040 సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: B. 0.10 సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. Steel grade, d'/D ratio and the distribution of longitudinal reinforcement సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: A. p/fck సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: C. 200 kN·m సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: B. The section is adequate with respect to this interaction check because the demanded moment is below the available moment capacity at the same Pu సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: B. The section is inadequate for the stated Pu-Mu combination and requires redesign సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: C. 135 kN·m సమాధానం: C.
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Question 20 ప్రశ్న 20Answer: B. Concrete tension is ignored in the sectional strength calculation సమాధానం: B.
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Question 21 ప్రశ్న 21Answer: C. 0.00275 సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: A. By setting ε = 0.0035 - 0.75ε, which gives ε = 0.002 సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: C. No, because both force equilibrium and moment equilibrium must be satisfied సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: B. It is generally nonlinear because concrete and reinforcement stresses change with the strain profile and neutral-axis position సమాధానం: B.
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Question 25 ప్రశ్న 25Answer: C. Concentric or purely axial compression capacity సమాధానం: C.
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Question 26 ప్రశ్న 26Answer: A. Pure bending without net axial force సమాధానం: A.