The crippling stress of a stiffener flange depends principally on
Answer: A
A wide, thin flange with one free edge buckles at a much lower stress than a narrow one supported on both edges. Standard methods break the section into elements, assign each a crippling stress, and take an area-weighted average for the whole.
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An idealisation for a compression-critical panel must account for
Answer: B
The two interact: the stiffener's crippling stress sets how hard it can be worked, and that stress in turn determines how much skin remains effective. An iterative calculation is usually needed to settle both together.
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A stiffener flange of width \( 25 \) mm and thickness \( 2 \) mm has a width-to-thickness ratio of
Answer: C
Correct answer: 12.5
The ratio is width over thickness:
\[ \frac{25}{2} = 12.5 \]This is the parameter that governs local buckling of the flange, and hence the crippling stress of the section. A slender flange, with a high ratio, cripples at a low stress; a stocky one may reach yield before buckling locally, which is the practical upper limit on how efficient the section can be.
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Two stiffener elements have crippling stresses of \( 240 \) and \( 300 \) MPa with areas of \( 100 \) and \( 200 \) mm\( ^2 \). The section crippling stress is nearest to
Answer: D
Correct answer: 280 MPa
The section crippling stress is the area-weighted average of its elements:
\[ \sigma_{cc} = \frac{240(100) + 300(200)}{100 + 200} = \frac{84\,000}{300} = 280 \ \mathrm{MPa} \]The weighting matters - the simple average of 270 would understate the section, because the stronger element is twice the size. Each element buckles at its own stress and sheds load; the section stress is what the whole develops when they are combined.
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Assertion (A): A compression panel idealisation usually requires iteration.
Reason (R): The effective skin width depends on the stiffener stress, which itself depends on the effective area.
Select the correct answer from the options below.
Answer: A
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the circularity. The effective width depends on the stiffener stress, and the stiffener stress is the load divided by the effective area, which includes that effective width. Neither can be found without the other, so the calculation is begun with an assumed stress and repeated until the two agree - usually two or three passes are enough.
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Assertion (A): The uprights of a diagonal tension field beam carry loads absent from an unbuckled beam.
Reason (R): The inclined tension bands pull the flanges inward and compress the uprights.
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 mechanism. Once the web buckles in shear it can no longer carry diagonal compression, so the shear is carried instead by inclined bands of tension. Those bands pull the flanges towards each other and place the uprights in compression - loads that simply do not exist in a beam whose web has not buckled. The uprights must therefore be designed as columns, which is Wagner’s tension field theory.
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Consider the following statements about crippling:
1. It is local buckling of the stiffener flanges.
2. It occurs at a stress that may be below the material's yield.
3. It depends on the flange width-to-thickness ratio.
Which of the statements given above is or are correct?
Answer: C
Correct answer: 1, 2 and 3
All three are correct and together they define crippling. It is local buckling of the flanges and webs of a stiffener rather than of the member as a whole; it can and usually does occur below the material’s yield stress, which is why crippling rather than yield is the compressive allowable; and it is governed by the width-to-thickness ratio of each element, which is what the empirical crippling curves are plotted against.
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Consider the following statements about a compression-critical stiffened panel:
1. Effective width depends on the stiffener stress.
2. Crippling stress limits how hard the stiffener can be worked.
3. The two effects can be assessed entirely independently.
Which of the statements given above is or are correct?
Answer: D
Correct answer: 1 and 2 only
Statements 1 and 2 are correct: effective width depends on the stiffener stress, and crippling caps how hard the stiffener can be worked. Statement 3 is wrong, and it is the practical point - the two are coupled, since the effective area determines the stress and the stress determines the effective area, so the panel is sized by iterating on both together rather than by treating each on its own.
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Match each instability in List I with what governs it in List II.
List I
A. Skin buckling
B. Stiffener crippling
C. Column buckling of a stiffener
D. Diagonal tension field
List II
1. Flange width-to-thickness ratio
2. Panel width, thickness and edge support
3. Post-buckled shear behaviour of a thin web
4. Slenderness ratio and end fixity
Select the correct match.
Answer: A
Correct answer: A-2, B-1, C-4, D-3
Four instabilities, each with its own governing parameter. Skin buckling depends on the panel width, thickness and the support along its edges. Stiffener crippling depends on the flange width-to-thickness ratio. Column buckling of the stiffener depends on its slenderness ratio and end fixity, through the Euler relation. And diagonal tension is the post-buckled behaviour of a thin shear web, described by Wagner’s theory.
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Which of these is NOT a consequence of designing a web to work in diagonal tension?
Answer: B
Correct answer: The web itself must be made thicker
The reverse is the point: designing for diagonal tension allows a thinner web, since it need not be prevented from buckling, and that is where the weight saving comes from. What must be strengthened is everything around it - the uprights now carry compression from the tension bands, and the flanges are pulled inward and carry additional bending. The saving is real but smaller than the web thickness alone would suggest.
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