RAJALAKSHMI ENGINEERIMG COLLEGE

DEPARTMENT OF AERONAUTICAL ENGINEERING

QUESTION BANK

AE 2254 AIRCRAFT STRUCTURES-I

1. Explain the general criteria to determine whether the truss is statically determinate.

2. What are the primary and secondary stresses in the analysis of a truss?

3. A 20 cm long steel tube 15cm internal diameter and 1cm thick is surrounded by a brass tube of same length and thickness. The tubes carry an axial load of 150 kN. Estimate the load carried by each. Es = 210 GPa, Eb = 100 GPa.

4. Write down three moment equation in the general form.

5. Define stiffness factor in moment distribution method. ,

6. State Reciprocal theorem.

7. Give expression for strain energy

(a) Torsion

(b) Bending.

8. Differentiate long column from short column.

9. What is Southwell's plot?

10. A solid cube of steel (E = 210 GPa) is subjected to a tension 150 MPa, find the strain energy per unit volume.

11. Explain the general criteria to determine whether the truss IS statically determinate.

12. What are the primary and secondary stresses in the analysis of a truss?

13. A 20 cm long steel tube 15cm intemal diameter and 1cm thick is surrounded by a brass tube of same length and thickness. The tubes carry an axial load of 150 kN. Estimate the load carried by each. Es = 21. 0 GPa, Eb = 100 GPa.

14. Write down three moment equation in the general form.

15. Define stiffness factor in moment distribution method.

16. State Reciprocal theorem.

17. Give expression for strain energy

(a) Torsion (b) Bending.

18. Differentiate long column from short column.

19. What is Southwell's plot?

20. A solid cube of steel (E = 210 GPa) is subjected to a tension 150 MPa, find the strain energy per unit volume.

21. What is the slope at free end of a cantilever beam of length Land uniform El when it is subjected to a load P at the free end?

22. A cantilever beam of uniform El is subjected to moment M at the free end. Sketch the load of the corresponding conjucate beam?

23. Explain the use ofClampeyron's three moment theorem?

24. Explain what is m~ant by distribution lactor?

25. A cantilever beam of length L and uniform El is subjected to a concentrated load to the free end. Explain how the slope at the free end is obtained using Castigliano's theorem?

26. State and explain Maxwell's reciprocal theorem?

27. Explain what is meant by beam of uniform strength?

28. The cross section of a column is rectangular of width 50 mm and depth 100 mm. What is the value for second moment of area that must be used for buckling load calculation?

29. Define the slenderness ratio for a column of circular section.

30. Define beam column with suitable example.

31. Explain the general criteria to determine whether the truss IS statically detenrunate.

32. What are the primary and secondary stresses in the analysis of a truss?

33. A 20 cm long steel tube 15cm intemal diameter and 1cm thick is surrounded by a brass tube of same length and thickness. The tubes carry an axial load of 150 kN. Estimate the load carried by each. Es = 210 GPa, Eb = 100 GPa.

34. Write down three moment equation in the general form.

35. Define stiffness factor in moment distribution method.

36. State Reciprocal theorem.

37. Give expression for strain energy(a) Torsion(b) Bending.

38. Differentiate long column from short column.

39. What is Southwell's plot?

40. A solid cube of steel (E = 210 GPa) is subjected to a tension 150 MPa, find the strain energy per unit volume.

41. Explain, with suitable example, the difference between a frame and a truss.

42. What is the condition for a plane truss to be stable or not with respect to the number of members and the joints?

43. What is a composite beam?

4. Explain the carry over factor, distribution factor and stiffness factor in moment distribution method.

5. Explain the dummy unit load method of determining deflections of a: point in a structure.

-6. Give the strain energy expressions for a member subjected to axial, bending, shear and torsional loads.

,7. Explain how'the Euler's column curve is not valid for short columns.

8, What is a beam column? Give some examples in aircraft structures for such columns.

9. What is the need for knowing the maximum shear stress when a structural member is subjected only normal stresses?

10. List down various failure theories and explain their applications for a particular case,

44.

4.5.PART B - (5 x 16 = 80 marks)

11. (a) Find the forces in the members of the truss shown in the fig. 1 .byany one method.

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Fig. 1 Or

(b) The truss shown in fig. 2 is supported as cantilever at the joints A and H. Find the forces in the members.

Fig. 2

12. (a) Find the support moments and draw bending moment diagram of the continuous beam shown in the fig. 3 using three moment equation.

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Fig. 3 Or

(bY Find the support moments and draw bending moment diagram of the continuous beam shown in the fig. 3 using moment distribution method.

2 J3008

6.13. (a) (i) Find the deflection at the mid-point of a siniply supported beam of length L,

subjected to a uniformly distributed load using unit load method. (8)

(ii) Find the redundant force in the member OC of the truss' shown in fig. 4 (8)

Fig. 4

Or

(b) For the truss shown in the fig. 5, the cross section area of bars in compression are 30 cm2 and others 12 cm2

• Determine the vertical displacement of point C and horizontal displacement of point B. Given: E = 210 GPa

~II

Fig. 5

14. (a) A thin circular ring of radius R and bending rigidity EI is subjected to three symmetric radial compressive loads lying in the plane of the ring structure. Obtain the expression for the bending moment and plot its distribution.

Or

(b) Find the buckling stress of a hinged-hinged column of length 100 em and having T-cross section. The dimensions of the flange are 10 em x 2 em and the web 10 cm x 2 em. Derive the formula used. E = 70 GPa.

3

J3008

15. (a) A beam-column made-of steel (E = 210 GPa) siml'ly supported at both ends is subjected to a uniformly distributed load of 500 N/m and an axial load of 1000 N. Find the moment at any section and hence find the maximum stress. Given: L = 4 m, b = 20 nun, d :; 40 mID.

Or

(b) A circular shaft of tensile yield strength 350 MPa is subjected to a combined state of loading defined by a bending moment M = 15 kN-m and Torque T = 10 kN-m. Calculate the diameter d which the bar must have in order to achieve a factor of safety N = 2. Apply the following theories.

(i) Maximum

shear stress

theory

(

ii) Maximum

distorsion energy

theory (iii) Octahedral

shear stress theory.

.a)i) bending.

Derive the expression for strain energy stored in a

beam,due to (4)

14.b) OR

A propped cantilever beam AB of length Land unifom1 EI is subjected uniformly distributed load of intensity q N/m and a concentrated load W at its mid-point. The beam is fixed at A and on roller support at B. Using Castigliano's theorem or any other method compute the reaction forces at the support points A and B.

Derive the expression for Rankine's formula

ii) Compare the buckling loads gIven by Rankine's and Buller's formulae for a

tabular column 2.25m long having outer dia:l1eter 37.5mm and inner diameter 32.5mm and both ends are pin ended

joints. Assume yield stress to be 315 mpa, Rankine's constant is _1_ 7500

aced E= 200 Gpa. (12)

OR

15.b )i) end (6)

Derive the expression for buckling load for a column with one fixed and the other end free.

l5.a)i) (4)

ii) Determine the ratio of buckling loads of two columns of circular cross-section one hollow and the etuer solid when both are made of same material, have same length, cross-section area and end conditions. The inner diameter of hollow column is half

its outer diameter. (6)

11. A beam of length L and uniform EI is simply supported at its end~ and subjected to a load W at a distance 'a' from left end. Obtain deflection at the mid point and at the point of application of the load using double integration method or area moment method?

12.a) A beam is simply supported at its ends. It is of length Land EI is uniform and subjected to a load D at the mid point of the beam. Using conjucate beam method compute slope at he support and maximum deflection.

OR

12.b) A timber beam 16 cm wide and 20 cm deep is to be reinforced by steel strips each 16 cm wide and 1 cm thick. Find the moment of resistance when (i) the steel strips are attached at the top and bottom so that overall all depth is 22 cm and (ii) the steel strips are attached symmetrically at the sides so that overall width is 18 cm. Allowable stress in the timber is 6 mpa.

13.a)i) Derive the expression for three moment equation. (4) ii) A simply supported beam ABC is of length 6 m and supported

at A, B, and C. AB = 3.6 m and Be = 2.4 m. A load of 2 kN is applied at 1.8 m from A and another load of 4 kN is applied at 1.8 m from C. Assuming EI is constant compute reactions at the support points. (12)

OR 13.b) Obtain the reaction at the support points of the beam shown in fig. I.

Using moment distribution method. 900 N

2 knlm l §F o·srn· 1 OArn C O.4rn ~ '/"'A~, D

B

12. ([;1) State and pi-bve Clapeyr'on's3.:c.moinent-equrltibn.' .... , :" ~. ' ..

Or ".

(b) Determine all support react~ons for the beam shown in Fig. 5' Use Clapeyron's 3-moment equation. Then, draw the shear force and bending moment diagrams. EI is const;:int.

Fig. 5

13, (a) (i) State the prove Castigliano's theorems. (6) (il) Using energy methods, determine the slope at point B of the beam

shown in):')g.)3:E:;:, 210 GPa. I=10:-41n4. (10)

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(b) Determine all the support' reactions of the beam shown in Fig. 7 using energy methods. The~ draw the shear force and bendi~g moment diagrams. E= 210 GPa. I=10,,4m 4.

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Fig. 7

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-J 14. (a) (i) Derive and obtain the first 2 buckled shapes and corresponding

buckling loads of a fixed-fixed column. (10) . , . .

(ii) Explaiil Rankine's hypothesis. (6) 'il

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. (b) Write notes on the following tOPICS (i) Inelastic column buckling. (10)

(ii) The Southwell plot. (6)

15. (a) What is a beam-column? Where can a .. beam-colu~nn type of structure be found in an aircraft? Explain the structural analysis of a beam -column type of structure, with an example.

Ot

(b) . (i)

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Explain the maximum distorti9n energy failure theory. Refer Fig. 8. • ." '." - .• :., .;. ,;.,". "",: .•• ~.', ;, '. '-.,,:' '" I. ", i :".J , ," r· '.'"". -·r ,'. t '~.'

Point A is a critical poinl located on the top surface of the lever arm. Determine the max.imum load Po according to the maximum distortion energy failure theory udng a factor of safety of 1.5. The sho9.£1. is mad6 of ste-cl w.i.Lh a yieldistress value. of 300 MPa. . (10)

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Fig. 8 .

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(ii) Explain the maximum principal stress theory of failure. (6)

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