Structural Idealisation Questions and Answers

Answer: C

Correct answer: 534 mm²

The stringer takes its own area plus the effective skin on both sides:

The skin contributes more than the stringer itself here, which is typical and is why the effective width calculation matters so much. Counting one side only gives 392, and omitting the skin altogether gives 250.

Answer: D

A change of well under one per cent on refinement is evidence that the discretisation error is already small for that quantity. It is exactly the convergence argument used to justify a mesh density in a finite element model.

Answer: A

Agreement to about two parts in a thousand is consistent with numerical rounding and reporting precision. A discrepancy of a few per cent or more would instead point to a misapplied load, an unintended restraint or a units error.

Answer: B

Correct answer: One quarter of the total

The model represents one quarter of the structure, so it must be given one quarter of the load; the symmetry conditions on the cut faces then reproduce the effect of the three quarters left out. Applying the full load would overstate the answer fourfold. The reactions in the model likewise sum to a quarter of the total, which is what the equilibrium check must be made against.

Answer: C

The two effective strips total \( 142 \) mm, leaving \( 180 - 142 = 38 \) mm of buckled skin in the middle carrying essentially no direct stress. Widening the stiffener spacing further simply adds more unworking material.

Answer: D

Correct answer: 20

The refinement ratio is the global element size over the submodel element size:

A ratio of this order is usual, and the submodel is driven by displacements interpolated from the global solution on its cut boundaries. The boundary must be placed far enough from the region of interest that the coarse model’s displacements there are trustworthy - Saint-Venant’s principle again.

Answer: A

Effective width is directly proportional to thickness in the von Karman expression, so doubling the thickness doubles it. If the stress also changed the square root term would modify this, but at constant stress the relationship is simply linear.

Answer: B

Each boom lies \( 100 \) mm from the axis, so \( I = 4 \times 400 \times 100^2 = 1.6 \times 10^7 \) mm\( ^4 \). Adding effective skin areas to each boom would raise this, which is precisely why the effective width matters.

Answer: C

Each boom now has \( 534 \) mm\( ^2 \), so \( I = 4 \times 534 \times 10^4 = 2.14 \times 10^7 \) mm\( ^4 \), about a third more than the bare stringers alone. Neglecting the working skin would therefore understate the stiffness appreciably.

Answer: D

A twelve per cent shift means the discretisation error is still large, so nothing about either result can be trusted yet. Refinement continues until successive results agree to within a tolerance appropriate to the decision the number will support.