Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III AIRCRAFT STRUCTURAL ANALYSIS Previous Question Paper (March - 2021 - R16)
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Main
Determine the buckling strength of a panel, comprising flat sheet and uniformly spaced Z-section stringers, a part of whose cross section is shown in Figure 1, under uniform compressive loads.
Answer
The buckling strength of a panel with Z-section stringers under uniform compression is determined by considering the combined stability of the skin and the stringers. The analysis relies on the concept of effective width of the skin, as the skin between stringers buckles at a stress lower than the ultimate failure stress of the panel.
The critical buckling stress of the skin is given by:
where K is the buckling coefficient (typically 4.0 for long plates), E is Young's modulus, ν is Poisson's ratio, t is the skin thickness, and b is the stringer spacing.
To calculate the total buckling strength, follow these steps:
- Determine the effective width (we) of the skin that remains effective after buckling using Von Karman's formula: we = 1.9t * sqrt(E / σmax).
- Calculate the effective area of the panel cross-section (Aeff) by summing the area of the Z-stringers and the effective width of the skin attached to each stringer.
- Calculate the overall buckling load (Pcr) of the stiffened panel acting as a column using the Euler buckling formula: Pcr = π2 E Ieff / (Le2), where Ieff is the moment of inertia of the effective cross-section about the neutral axis and Le is the effective length of the panel.
- The ultimate strength is reached when the stress in the stringer or the effective skin reaches the yield stress or the crippling stress of the Z-section.
The total buckling strength is the minimum of the local skin buckling load and the global panel instability load, adjusted for the reduced stiffness provided by the post-buckled skin.
Find the compression buckling stress for a sheet 10cm x 10cm x 3mm with all four edges simply supported, assuming Et = 55 GPa.
Answer
The critical buckling stress for a rectangular plate with all four edges simply supported is given by the formula:
Where:
- a = 10 cm (length)
- b = 10 cm (width)
- t = 0.3 cm (thickness)
- E = 55 GPa = 55,000 MPa
- ν = Poisson's ratio (typically 0.3 for aluminum alloys)
- k = buckling coefficient
For a square plate (a/b = 1) with all edges simply supported, the buckling coefficient k is 4.0.
Substituting the values into the formula:
The compression buckling stress for the given sheet is approximately 178.93 MPa.
A Z- section with 12 cm x 3 cm flanges and 20 cm x 3 cm web is subjected to Mx=10 kN-m and My=10 kN-m. Determine the maximum bending stress.
Answer
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Determine the shear flow distribution on the bottom flange in the thin-walled Z section shown in Figure 2 due to a shear load Sy applied through the shear center of the section.
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Explain the structural idealization for a typical wing section and derive the expression for boom areas of a typical wing skin (width b and thickness t) with two adjacent booms.
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The fuselage section shown in figure 3 is subjected to a bending moment of 100 kNm applied in the vertical plane of symmetry. If the section has been completely idealized into a combination of direct stress carrying booms and shear stress only carrying panels, determine the direct stress in each boom.
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Define shear lag and write the equilibrium equations with free body diagrams for Six-Boom beam subjected to a shear load.
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Find the shear flow in each web of the beam shown in the Figure 4. Plot the distribution of axial load along each stiffening member when P1=20kN, P2=15kN and P3=10kN. All dimensions are in cm.
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