GATE Ae : Test-I - 30 June 2020

25 Questions | Total Attempts: 24

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GATE Ae : Test-I - 30 June 2020

GATE AE : Structures 30 JUNE 2020 3:00 pm Duration : 90 min Strength of Materials / Aircraft Structures Topic-I : Axially loaded members


Questions and Answers
  • 1. 
    A rod of length L having uniform cross sectional area A is subjected to a tensile force P as shown in the figure below. If the Young's modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the section S-S is:   [Choose the correct option as given in the answer choice] Options: A. P/A                          B.                              C.                             D.     
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 2. 
    The figure below shows a steel rod of 25 mm2 cross sectional area. It is loaded at four points K,L,M and N. Assume Esteel = 200GPa. The total change in length of the rod due to loading is equal to:
    • A. 

      1 m

    • B. 

      -10 m

    • C. 

      16  m

    • D. 

      -20  m

  • 3. 
    A uniform slender cylinder rod made of homogeneous and isotropic material rests on a friction less surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by  and  respectively, then.....
    • A. 

       

    • B. 
    • C. 

       

    • D. 

       

  • 4. 
    The stress-strain behaviour of a material is shown in the figure. Its toughness and resilience in kN/m2 are __________ and ___________ respectively.   (Note here that the Stress (in MPa) values for strain 0.004, 0.008, 0.012 are 70, 90, 120 respectively)  
    • A. 

      280 and 760

    • B. 

      280 and 900

    • C. 

      760 and 140

    • D. 

      900 and 140

  • 5. 
    Consider the structural system shown in the figure under the action of weight W. All the joints are hinged. The properties of the members in terms of length (L), area (A) and the modulus of elasticity (E) are also given in the figure. Let L, A and E be 1 m, 0.05 m2 and 30 × 106 N/m2 respectively, and W =100 kN.   Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member QR?
    • A. 

      Compressive force = 25kN; Stress = 250kN/m2 ; Shortening = 11.8mm

    • B. 

      Compressive force = 14.14kN; Stress = 141.4kN/m2 ; Shortening = 11.8mm

    • C. 

      Compressive force = 72.4kN; Stress = 724kN/m2 ; Shortening = 41.7mm

    • D. 

      Compressive force = 100kN; Stress = 1000kN/m2 ; Shortening = 41.7mm

  • 6. 
    A cantilever rod of length L and circular cross-section 'A' has modulus of elasticity 'E' and coefficient of thermal expansion 'α'. If the temperature of the rod is increased by  △T, then which of the following is true?
    • A. 

      Thermal stress developed in the rod is αE△T and thermal strain is  α△T

    • B. 

      Thermal stress in the rod is αE△T and thermal strain is αL△T

    • C. 

      Thermal stress developed in the rod is zero and thermal strain is α△T

    • D. 

      Both thermal stress and thermal strain developed in the rod are zero

  • 7. 
    A steel cube with all faces to deform, has Young's modulus 'E', Poisson's ratio 'ν' coefficient of thermal expansion 'α' . The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature ΔT is given by: (Choose the correct option as given in the answer choice) Options:
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 8. 
    Below figure shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steel wires. Neglect the weight of the beam, The tension T1 and T2 induced in the wires due to vertical load P as shown are.....
    • A. 

      T1 = P/2,  T2 = P/2

    • B. 
    • C. 
    • D. 
  • 9. 
    A bar having a cross sectional area 700mm2 is subjected to axial loads as indicated. The value of stress in the segment QR is:
    • A. 

      40 MPa

    • B. 

      50 MPa

    • C. 

      70 MPa

    • D. 

      120 MPa

  • 10. 
    Numerical Answer Type question: In the figure, the load P= 1kN, length L = 1m, Young's modulus E = 70GPa, and the cross section of the links is a square with dimensions 10mm x 10mm. All joints are pin joints. The stress (in Pa) in the link AB is _______________. (Indicate compressive and tensile stress with a appropriate sign) [Type the correct numerical answer in the space provided below]
  • 11. 
    Numerical Answer Type Question: A horizontal bar fixed at one end (x=0) has a length of 1m, and cross sectional area 100mm2. Its elastic modulus varies along its length as E(x) = 100e-x GPa where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10kN is applied at the free end, the axial displacement of the free end is ________________mm.  [Type the numerical answer rounded off to two decimals in the space below]
  • 12. 
    A point mass of 100kg is dropped onto a massless elastic bar (A = 100mm2, L = 1m, E = 100GPa) from a height of 10mm as shown. If g=10m/s2, the maximum compression of the elastic bar is ___________mm.
    • A. 

      1.73

    • B. 

      1.46

    • C. 

      1.52

    • D. 

      1.65

  • 13. 
    Numerical Answer Type question: A bimetallic cylindrical bar of cross sectional area 1m2 is made by bonding steel (E = 210GPa) and Aluminium (E = 70GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10-6 in steel bar and compressive axial strain of 10-6 in aluminium bar, the magnitude of the required force (in kN) in indicated direction is ___________. [Type the numerical answer in the space below]
  • 14. 
    Two bars of different Young's moduli E1 and E2 but with same cross section area 'A' and coefficient of thermal expansion 'α'  are attached together at one end and fixed at other as shown in the fig. The construction of this setup was carried out at an ambient temperature of 25oC.  The stress in the bars when the temperature is increased uniformly by 10oC is: (Choose the correct option as given in the answer choice)
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 15. 
    A horizontal rod of length L of circular cross section with diameter d is subjected to a compressive axial load P. Young's modulus : E. The energy absorbed by the rod due to loading is given by:  (Select the correct option as given in the answer choice)
    • A. 

      A

    • B. 

      B

    • C. 

      C

    • D. 

      D

  • 16. 
    A uniform bar of length L, cross-sectional area A, and mass density p is suspended vertically from one end. Find the elongation of the bar due to its own weight. Young's modulus : E, gravitational acceleration : g
    • A. 

      PgL2/AE

    • B. 

      PL2/gE

    • C. 

      PgL2/2E

    • D. 

      L2g/pE

  • 17. 
    A solid cylinder of diameter D carries an axial compressive load P. The increase in the diameter of the cylinder is ____________. [Young's modulus : E, Poisson's ratio : v]
    • A. 

      Pv/πED

    • B. 

      2Pv/πED

    • C. 

      4Pv/πED

    • D. 

      Pv/2πED

  • 18. 
    Numerical Answer Type question: Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure. Segment 1 and 2 have cross-sectional area of 100 mm2 and 60 mm2, Young's modulus of 2 x 10MPa and 3 x 10MPa and length of 400 mm and 900 mm respectively. The strain energy (in N-mm, up to one decimal place) in the bar due to the axial load is ___________ [Type the answer correct to one decimal in the space below]
  • 19. 
    What is the ratio of elongations of tapered rod of length L, Young's modulus E having circular cross section with diameter varying along its length as 'd' at one end and '2d' at other end to that of another horizontal rod of same length, same modulus but with constant diameter equal to mean diameter of the tapered one, both when subjected to same axial load P?
    • A. 

      8/9

    • B. 

      9/8

    • C. 

      5/7

    • D. 

      7/5

  • 20. 
    A copper rod of 2 cm diameter is completely encased in a steel tube of inner diameter 2 cm and outer diameter 4cm. Under an axial load, the stress in the steel tube is 100 N/mm2 . If Es= 2Ec, then the stress in the copper rod is ___________.
    • A. 

      50 MPa

    • B. 

      33.33 MPa

    • C. 

      100 MPa

    • D. 

      300 MPa

  • 21. 
    Numerical Answer type question: In the arrangement as shown in the figure, the stepped steel bar ABC is loaded by a load P. The material has young’s modulus E=200 GPa and the two portions AB and BC have area of cross section 1 cm2 and  2 cm2 respectively. The magnitude of load P (in kN) required to fill up the gap of 0.75 mm is ____________. [Type the correct numerical answer in the space below]
  • 22. 
    The stress-strain curve for mild steel is shown in the figure. Choose the correct option referring to both figure and table:
    • A. 

      P-1, Q-2, R-3, S-4, T-5, U-6

    • B. 

      P-3, Q-1, R-4, S-2, T-6, U-5

    • C. 

      P-3, Q-4, R-1, S-5, T-2, U-6

    • D. 

      P-4, Q-1, R-5, S-2, T-3, U-6

  • 23. 
    Numerical Answer Type: A rigid bar of negligible weight is shown in the figure. If W = 80kN, the temperature change (in oC) of the assembly that will cause a tensile stress of 50MPa in the steel rod is __________. (Use the following data) :   [Type the answer correct to one decimal place in the space below- indicate temperature increase and decrease with positive and negative sign resp.]
  • 24. 
    Numerical Answer Type: The rigid bar AB, attached to aluminum and steel rods is horizontal before the load P is applied. Find the vertical displacement of point C (in mm) caused by the load P = 50 kN. Neglect all weights. [Type the answer correct to two decimal places in the space below]
  • 25. 
    Numerical Answer Type: A 9kN tensile load is applied to 50m length steel wire with E = 200GPa. The normal stress in the wire must not exceed 150MPa and the increase in length of the wire should be at most 25mm. What is the smallest diameter (in mm) of the wire so that the wire does not fail? [Type the answer correct to two decimal places in the space below]
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