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Question 1
ప్రశ్న 1
Which loading condition represents biaxial bending of an RCC column?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Biaxial bending occurs when a compression member is subjected to bending about two axes simultaneously. The member therefore carries an axial compressive force together with two bending-moment components. The resulting strain distribution is more complex than that for a uniaxially bent column. Capacity about one axis cannot generally be checked independently of the demand about the other axis. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
A column carries a factored axial load of 1200 kN together with moments Mux = 96 kN·m and Muy = 72 kN·m. What are the equivalent eccentricities Mux/Pu and Muy/Pu respectively?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The equivalent eccentricity associated with each moment is obtained by dividing that moment by the axial load. For the x-axis moment, 96/1200 = 0.08 m, which is 80 mm. For the y-axis moment, 72/1200 = 0.06 m, which is 60 mm. These eccentricities illustrate why bending exists simultaneously about the two axes. Therefore Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
According to IS 456, how may the resistance of a column under combined axial load and biaxial bending be determined directly without using the simplified interaction equation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
IS 456 permits a fundamental sectional analysis for combined axial compression and biaxial bending. The neutral axis has to be selected so that the internal forces satisfy the applied axial load. The internal moments must simultaneously satisfy equilibrium about both relevant axes. This generally requires an iterative strain-compatibility and equilibrium procedure. Therefore Option B is correct.
వివరణ:
Question 4
ప్రశ్న 4
Which expression is the IS 456 alternative interaction relationship for a member subjected to axial compression and biaxial bending?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
IS 456 provides an interaction equation as an alternative to a full biaxial sectional analysis. The applied moments are normalized by the corresponding uniaxial moment capacities at the same axial load. Each normalized moment ratio is raised to the exponent αn. The sum of those two terms must not exceed unity. Therefore Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
In the IS 456 biaxial interaction equation, what do Mux1 and Muy1 represent?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mux1 and Muy1 are not arbitrary independent column capacities. Each is the maximum uniaxial moment capacity corresponding to the actual axial load Pu being considered. Mux1 relates to uniaxial bending about the x-axis and Muy1 to bending about the y-axis. Their values can differ because section dimensions and reinforcement distribution may differ about the two axes. Therefore Option C is correct.
వివరణ:
Question 6
ప్రశ్న 6
Which expression defines Puz for determining the exponent αn in the IS 456 biaxial interaction relationship?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The biaxial interaction exponent is related to the ratio Pu/Puz. IS 456 defines Puz as 0.45fckAc + 0.75fyAsc for this purpose. This expression should not be confused with the simplified short axially loaded tied-column equation. Ac represents the concrete area and Asc represents the longitudinal steel area. Therefore Option B is correct.
వివరణ:
Question 7
ప్రశ్న 7
A 400 mm × 500 mm column contains 3000 mm² of Fe415 longitudinal reinforcement and uses M25 concrete. What is Puz approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The gross section area is 400 × 500 = 200000 mm². Hence the concrete area is 200000 - 3000 = 197000 mm². The concrete contribution is 0.45 × 25 × 197000 = 2216.25 kN, while the steel contribution is 0.75 × 415 × 3000 = 933.75 kN. Their sum is 3150 kN. Therefore Option C is correct.
వివరణ:
Question 8
ప్రశ్న 8
For a biaxially loaded column, Pu/Puz = 0.15. What value of αn is used in the IS 456 interaction equation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
IS 456 relates αn to the axial-load ratio Pu/Puz. When that ratio is less than 0.2, αn is taken as 1.0. Linear interpolation is required only between ratios of 0.2 and 0.8. The value does not reduce below 1.0 for still smaller axial-load ratios. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
For a column with Pu/Puz = 0.50, what value of αn is obtained by the IS 456 linear interpolation rule?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The exponent increases linearly from 1.0 at Pu/Puz = 0.2 to 2.0 at Pu/Puz = 0.8. A ratio of 0.50 lies exactly halfway between 0.20 and 0.80. The corresponding exponent therefore lies halfway between 1.0 and 2.0. This gives αn = 1.5. Therefore Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
For a biaxially loaded column with Pu/Puz = 0.90, what value of αn should be used?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The interpolated range for αn extends only from Pu/Puz = 0.2 to 0.8. At and beyond the upper range, the exponent is taken as 2.0. Since the stated axial-load ratio is 0.90, it exceeds 0.8. The interaction relation therefore uses αn = 2.0. Therefore Option D is correct.
వివరణ:
Question 11
ప్రశ్న 11
For a column having αn = 1.0, the applied moment ratios are Mux/Mux1 = 0.35 and Muy/Muy1 = 0.55. What does the IS 456 biaxial interaction check indicate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
With αn equal to 1.0, the interaction terms are simply the two moment ratios themselves. Their sum is 0.35 + 0.55 = 0.90. The IS 456 requirement is that the interaction value should not exceed 1.0. Since 0.90 is less than unity, the stated biaxial strength check is satisfied. Therefore Option B is correct.
వివరణ:
Question 12
ప్రశ్న 12
A column has αn = 2.0, Mux/Mux1 = 0.80 and Muy/Muy1 = 0.65. Which conclusion follows from the biaxial interaction equation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For αn = 2.0, the interaction value is the sum of the squares of the two ratios. It equals 0.80² + 0.65² = 0.64 + 0.4225 = 1.0625. The individual ratios being below one is not sufficient for biaxial adequacy. Because the combined interaction value exceeds unity, the section fails this strength check. Therefore Option C is correct.
వివరణ:
Question 13
ప్రశ్న 13
For a column with αn = 1.5, the two normalized moment ratios are both 0.60. What is the approximate biaxial interaction value and conclusion?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The interaction value is 0.60^1.5 + 0.60^1.5. Each term is approximately 0.4648. Their sum is therefore approximately 0.9295. Since this value is below the limiting value of 1.0, the stated biaxial strength combination is acceptable. Therefore Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
When evaluating the IS 456 biaxial interaction equation, why is it incorrect to use a uniaxial moment capacity determined for an axial load different from the actual Pu?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Column moment capacity changes substantially with the level of axial compression. The interaction equation therefore defines Mux1 and Muy1 at the particular axial load Pu under consideration. Using capacities from a different axial-load level would distort the normalized moment ratios. Such a substitution could make an unsafe section appear adequate or vice versa. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
A rectangular RCC column is substantially deeper in one direction than the other. Which statement is correct regarding Mux1 and Muy1 at a given Pu?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A rectangular column generally has different flexural properties about its two principal axes. Reinforcement lever arms and the distribution of longitudinal bars can also differ in their effectiveness about those axes. Consequently, the uniaxial capacity corresponding to bending about one axis need not equal that about the other. Biaxial interaction explicitly accommodates these separate capacities. Therefore Option B is correct.
వివరణ:
Question 16
ప్రశ్న 16
A column has effective-length ratios lex/D = 10 and ley/b = 14. How should it be classified for Limit State design?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A compression member is short only when both relevant effective-length ratios are less than 12. The first ratio of 10 satisfies the short-member criterion in its direction. The second ratio of 14 exceeds the limiting value. The member therefore has to be treated as slender in the direction corresponding to that larger ratio. Therefore Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
For a framed column whose unsupported length is 4.0 m and whose ends are permitted relative lateral displacement, Annex E recommends that the effective-length ratio should not be taken below 1.2 when the Annex E approach is used. What corresponding lower effective length does this imply?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Annex E distinguishes frames in which relative lateral displacement of the column ends is prevented from those in which it is not prevented. For the latter condition, the code recommends that the effective-length-to-unsupported-length ratio should not be taken below 1.2. Multiplying 4.0 m by 1.2 gives 4.8 m. A larger effective length may still result from the actual restraint conditions. Therefore Option C is correct.
వివరణ:
Question 18
ప్రశ్న 18
When may a column be regarded as braced in a particular plane according to the guidance accompanying the IS 456 slender-column provisions?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The terms braced and unbraced refer to overall lateral stability rather than to ordinary column ties. A column may be considered braced in a plane when an adequate structural system resists lateral displacement in that plane. Such resistance may be supplied by walls, bracing or suitable buttressing designed for the lateral forces. If that structural stability is not provided, the column should be treated as unbraced in the plane concerned. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
What is the fundamental IS 456 requirement for analysis of a slender compression member?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Slender columns develop additional effects because their deflection under load influences the internal moments and forces. IS 456 therefore requires these second-order effects to be represented in design. They may be captured directly by an analysis that includes the effect of deflections. If they have not been included in the structural analysis, the code-specified additional moments must be considered in the appropriate direction. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
Which expression gives the IS 456 additional moment Max for a column slender about the direction associated with effective length lex and section depth D?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Clause 39.7.1 gives a prescribed additional-moment expression when second-order deflection effects have not already been included in the analysis. For the direction associated with section depth D, the expression is PuD/2000 multiplied by the square of lex/D. The squared slenderness term causes the additional moment to increase rapidly as effective length increases. This moment is subsequently combined with the appropriate primary moment for design. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
Which expression gives the corresponding IS 456 additional moment May in the direction associated with column width b and effective length ley?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The additional-moment equations are written separately for the two orthogonal column directions. In the direction associated with width b, IS 456 uses May = Pub/2000 multiplied by the square of ley/b, where the notation means Pu multiplied by b. The equation therefore depends on axial load, section dimension and effective slenderness in that direction. It should not be evaluated using the dimension associated with the other principal axis. Therefore Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
A slender column carries Pu = 1800 kN. For one bending direction, D = 500 mm and lex = 7.5 m. Before applying any permitted reduction factor, what additional moment Max is obtained from IS 456 Clause 39.7.1?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The slenderness ratio in the stated direction is lex/D = 7500/500 = 15. The additional moment is PuD/2000 multiplied by 15². Using consistent units gives 1800 × 500/2000 × 225 = 101250 kN·mm. This equals 101.25 kN·m. Therefore Option C is correct.
వివరణ:
Question 23
ప్రశ్న 23
The same slender column carries Pu = 1800 kN, but in the orthogonal direction b = 400 mm and ley = 6.0 m. Before any permitted reduction, what additional moment May is obtained?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The effective slenderness ratio in this direction is ley/b = 6000/400 = 15. The additional moment is therefore Pu × b/2000 multiplied by 15². In consistent units this gives 81000 kN·mm. Converting to kN·m gives 81 kN·m. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
A braced slender column has no transverse loads between its ends. Its smaller end moment is M1 = -100 kN·m, its larger end moment is M2 = 250 kN·m, and the calculated additional slenderness moment is 60 kN·m. Using the IS 456 note to Clause 39.7.1, what design moment governs?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For the stated braced case, the initial moment is 0.4M1 + 0.6M2, taking the smaller end moment as negative for double curvature. This gives 0.4(-100) + 0.6(250) = 110 kN·m, which also exceeds the minimum initial moment of 0.4M2 = 100 kN·m. Adding the 60 kN·m additional moment gives 170 kN·m. However, IS 456 also requires the total moment including the initial and additional moments not to be less than M2, which is 250 kN·m. Therefore 250 kN·m governs and Option D is correct.
వివరణ:
Question 25
ప్రశ్న 25
For a slender-column additional-moment calculation, take Puz = 4000 kN, Pb = 2500 kN and Pu = 3000 kN. Using the IS 456 reduction factor k = (Puz - Pu)/(Puz - Pb), subject to k ≤ 1.0, what value of k is obtained?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
IS 456 Clause 39.7.1.1 permits the additional moments calculated from Clause 39.7.1 to be multiplied by k = (Puz - Pu)/(Puz - Pb), with k not exceeding 1.0. Here Pb is the axial load corresponding to the balanced strain condition specified by the code. The numerator is 4000 - 3000 = 1000 kN and the denominator is 4000 - 2500 = 1500 kN. Thus k = 1000/1500 = approximately 0.67, so Option C is correct.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: A. Axial compression accompanied by bending moments about both principal axes సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: B. 80 mm and 60 mm సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: B. By choosing a neutral axis that satisfies equilibrium of axial load and moments about both axes సమాధానం: B.
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Question 4 ప్రశ్న 4Answer: B. (Mux/Mux1)^αn + (Muy/Muy1)^αn ≤ 1.0 సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: C. The maximum uniaxial moment capacities about the respective axes at the same axial load Pu సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: B. Puz = 0.45fckAc + 0.75fyAsc సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: C. 3150 kN సమాధానం: C.
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Question 8 ప్రశ్న 8Answer: A. 1.0 సమాధానం: A.
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Question 9 ప్రశ్న 9Answer: C. 1.5 సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: D. 2.0 సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: B. Safe because the interaction value is 0.90 సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: C. Unsafe because the interaction value is approximately 1.063 సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 0.93; safe సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. Because Mux1 and Muy1 are specifically defined as capacities corresponding to the same Pu సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: B. They may differ because section geometry and reinforcement distribution influence capacity about each axis సమాధానం: B.
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Question 16 ప్రశ్న 16Answer: B. Slender in the direction associated with ley/b because that ratio exceeds 12 సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: C. 4.8 m సమాధానం: C.
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Question 18 ప్రశ్న 18Answer: B. When lateral stability of the structure as a whole in that plane is provided by walls, bracing or buttressing designed to resist the lateral forces సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: B. Deflection effects on moments and forces should be included, or the specified additional moments should be introduced where those effects were not included in the analysis సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: A. Max = PuD/2000 × (lex/D)^2 సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. May = Pub/2000 × (ley/b)^2 సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: C. 101.25 kN·m సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: C. 81 kN·m సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: D. 250 kN·m సమాధానం: D.
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Question 25 ప్రశ్న 25Answer: C. 0.67 సమాధానం: C.