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Stress Analysis of Wings and Fuselage Questions and Answers

41.

A member has an applied stress of \( 150 \) MPa and a margin of safety of \( 0.20 \). Its allowable is

Answer: A

Correct answer: 180 MPa

Rearranging the margin definition,

\[ \text{allowable} = \text{applied} \times (1 + MS) = 150 \times 1.20 = 180 \ \mathrm{MPa} \]

Adding 20 per cent of the allowable instead of the applied, or subtracting, gives the wrong figure - the margin is always taken on the applied stress, which is the denominator of the ratio.

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42.

Assertion (A): A wing section must be analysed for bending, shear and torsion together.

Reason (R): The air load produces all three actions simultaneously at every station.

Select the correct answer from the options below.

Answer: B

Both are true and the second explains the first. Direct stress from bending and shear flow from torsion act at the same point in the skin, and only combining them through a failure criterion gives a meaningful strength check.

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43.

Assertion (A): The von Mises criterion predicts no yielding under purely hydrostatic stress.

Reason (R): The criterion is based on distortion energy rather than total strain energy.

Select the correct answer from the options below.

Answer: C

Both statements are true and the second is the reason for the first. Hydrostatic stress changes volume without distorting the material, and experiment confirms that metals can sustain very large hydrostatic pressures without yielding.

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44.

Assertion (A): Margins of safety are quoted as a ratio less one rather than as a plain ratio.

Reason (R): Subtracting one makes zero the break-even point.

Select the correct answer from the options below.

Answer: D

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the purpose of the convention. Quoting the plain ratio would require every entry in a stress report to be compared mentally with unity; subtracting one puts the break-even at zero, so the sign alone says whether the member passes. Scanning a long table for negative numbers is far quicker and far less error-prone than scanning it for values below one.

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45.

Assertion (A): The end fasteners of a multi-row joint are the usual fatigue origins.

Reason (R): Differential stretching of the two sheets makes the outer rows carry more load.

Select the correct answer from the options below.

Answer: A

Both statements are true and the second is the reason for the first. The effect grows with the number of rows and with any stiffness mismatch, and tapering the sheet thickness towards the joint ends is one way of evening the sharing.

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46.

Assertion (A): A fitting factor is applied in addition to the ultimate factor of safety.

Reason (R): Load distribution within a fitting is less predictable than in a simple member.

Select the correct answer from the options below.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the justification. A simple member in tension carries a load that can be calculated with confidence; a fitting introduces eccentricities, uneven fastener load sharing, local bending and stress concentrations that the analysis represents only approximately. The fitting factor of about 1.15 covers that additional uncertainty, and it multiplies a load that already includes the ultimate factor of 1.5.

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47.

Assertion (A): Treating a fuselage frame as a free ring badly overstates its bending moments.

Reason (R): The surrounding skin feeds distributed shear into the frame all the way round.

Select the correct answer from the options below.

Answer: C

Both statements are true and the second is the reason for the first. The distributed reaction balances the applied load close to where it acts, so the real moments are far smaller than a free-ring idealisation predicts.

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48.

Assertion (A): B-basis allowables may be used for a member with redundant load paths.

Reason (R): B-basis figures carry ninety per cent survival at ninety-five per cent confidence.

Select the correct answer from the options below.

Answer: D

Both are true and the second gives the statistical meaning behind the first. Where a member's failure would be immediately critical, the more conservative A-basis value at ninety-nine per cent survival is required instead.

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49.

Assertion (A): The critical wing section for strength is usually near the root.

Reason (R): Both shear force and bending moment accumulate towards the root.

Select the correct answer from the options below.

Answer: A

Both statements are true and the second is the reason for the first. Inertia relief and greater structural depth both moderate the effect, but neither is enough to move the critical section outboard on a conventional wing.

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50.

Assertion (A): Load introduction at the wing-body joint requires heavy local structure.

Reason (R): Very large concentrated loads must be diffused into a shell only millimetres thick.

Select the correct answer from the options below.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the mechanism. The wing delivers its entire bending moment, shear and torque into the fuselage at a handful of attachment points, and that concentrated load must be spread into a shell of two or three millimetres without overstressing it locally. Diffusing it needs heavy machined fittings, thick doublers and closely spaced frames - which is why the centre section is among the heaviest parts of the aircraft per unit volume.

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