Hall Ticket No Question Paper Code: AAE002
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous) Dundigal, Hyderabad - 500 043
Four Year B. Tech III Semester End Examinations, November – 2018 Regulations: IARE - R16
THEORY OF STRUCTURES
(AERONAUTICAL ENGINEERING)
Time: 3 hours Max. Marks: 70
Answer ONE Question from each Unit All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT – I
1. a) A prismatic member of length l and unit weight w is suspended freely from its end.
Determine the elongation of the member under gravity.
[7M]
b) Draw bending moment and shear force diagram of a cantilever beam of 2m length carrying a point load of 800N at the free end.
[7M]
2. a) Describe the effects of temperature changes when a body is i. Free to deform
ii. Restrained
[7M]
b) A S.S.B of length 9m carries UDL of 10kN/m over a span of 6m from the left support. Draw shear force and bending moment diagram.
[7M]
UNIT – II
3. a) Explain the concept of simple bending and pure bending. What are the assumptions made is pure bending? Derive the expression of simple bending.
[7M]
b) A cantilever beam 60 mm wide by 200 mm high and 6m long carries a load that varies uniformly from zero at the free end to 1000N/m at the wall.
i. Compute the magnitude and location of the maximum flexural stress
ii. Determine the type and magnitude of the stress in a fiber 40 mm from the top of the beam at a section 3m from the free end.
[7M]
4. a) Show that for a rectangular cross section of the maximum shear stress is 1.5 times the average stress
[7M]
b) A cast iron beam section is of I-section with a top flange 80mm x 20mm thick, bottom flange 160mm x 40mm thick and the web 200mm deep and 20mm thick. The beam is freely supported on a span of 5m. If the tensile stress is not to exceed 20N/mm2, Determine the safe uniformly distributed load which the beam can carry.
[7M]
MODEL QUESTION PAPER
UNIT – III
5. a) Explain the concept of Double integration method to find the deflection in the beams [7M]
b) Calculate the Euler’s critical load for a strut of T-Section, the flange width being 10cm, overall depth 8cm and both flange and stem 1cm thick. The strut is 3m long and is built in at both ends. Take E= 2× 105N/mm2
[7M]
6. a) What are the assumptions made in Euler’s buckling theory? Derive the Euler’s buckling formula for long column.
[7M]
b) Determine the maximum deflections and support rotations in the beam shown in figure 1 using double integration method.
Fig.1
[7M]
UNIT – IV
7. a) A fixed beam of length L is loaded at third points by two point loads of W each.
Calculate the fixing moments using Maxwell’s reciprocal theorem and plot the Bending Moment and Shear Force diagrams.
[7M]
b) Determine the forces in all the members of the truss as shown in figure 2
Fig.2
[7M]
8. a) Derive expression for slope and deflection for a beam by Clapeyron’s theorem of three moments
[7M]
b) A cantilever beam ABCD covers three spans, AB=6m, BC=12m and CD=4m. It carries uniformly spread loads of 2KN, 1KN and 3KN per meter run on AB, BC and CD respectively. If the girder is of same cross-section throughout, find the bending moment at the supports B and C and the pressure on each support using Clapeyron’s theorem of three moments. Plot the B.M and S.F diagrams.
[7M]
UNIT – V
9. a) Derive the equations of static equilibrium and compatibility relations for a three dimensional elastic body.
[7M]
b) A structural member supports loads which produce, at a particular point a direct tensile stress of 80N/mm2 and a shear stress of 45N/mm2 on the same plane. Calculate the values and directions of the principal stresses at the point and also the maximum stress stating on which planes this will act.
[7M]
10 .
a) Derive the expression for major and minor principle stresses on an oblique plane, when the body subjected to direct stresses in mutually perpendicular directions accompanied by a shear stress.
[7M]
b) A cantilever of length L and depth 2h is in a state of plane stress. The cantilever is of unit thickness, is rigidly supported at the end x=L and is located as shown in figure 3.
Show that stress function Φ = Ax2+Bx2y+Cy3+D (5x2y3-y5) is valid for the beam and evaluate the constants A, B, C and D.
Fig.3
[7M]
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous) Dundigal, Hyderabad - 500 043
COURSE OBJECTIVES
The course should enable the students to :
S. No Description
I Understand various aspects of mechanics of materials as applied to engineering problems in a systematic manner stressing the fundamentals.
II Analyze problems on thermal stresses, shear force, bending moment and deflection of beams III Discuss the equilibrium and compatibility conditions for two-dimensional and three-
dimensional elastic bodies.
COURSE LEARNING OUTCOMES
Students, who complete the course, will be able to demonstrate the ability to do the following : CAAE002.01 Calculate the stress strain relations in conjunction with elasticity and material
properties
CAAE002.02 Describe the resistance and deformation in members which are subjected to axial, flexural and torsion loads.
CAAE002.03 Discuss thermal explanations in solid bars and induced thermal stresses
CAAE002.04 Solve for bending and shear stresses of symmetric and un-symmetric beams under loading conditions
CAAE002.05 Calculate the shear stresses developed in various sections of beams.
CAAE002.06 Calculate the flexural developed in various sections of beams of real field problems.
CAAE002.07 Differentiate between redundant structures and determinate structures.
CAAE002.08 Discuss the redundant complex structural components subjected to different loading and boundary conditions.
CAAE002.09 Solve for deflections of beams under loading with various approaches CAAE002.10 Calculate the stability of structural elements and determine buckling loads.
CAAE002.11 Discuss critical buckling load for column with various loading and end conditions CAAE002.12 Apply a theories and to predict the performance of bars under axial loading including
buckling.
CAAE002.13 Describe the behavior of structural components subjected to various loading and support conditions based on principles of equilibrium and constitutional relationships.
CAAE002.14 Explain the stress transformation and concept of principle plane and principle stresses CAAE002.15 Evaluate principal stresses, strains and apply the concept of failure theories for design CAAE002.16 Acquire Basic knowledge to solve real time problems in Aircraft structure with
different loading conditions
CAAE002.17 Apply the fundamental concepts of Theory of structures in competitive examinations.
MAPPING OF SEMESTER END EXAMINATIONS TO COURSE LEARNING OUTCOMES
SEE Question
No.
Course Learning Outcomes
Blooms’
Taxonomy Level 1
a CAAE002.01 Calculate the stress strain relations in conjunction with
elasticity and material properties Understand b CAAE002.01 Calculate the stress strain relations in conjunction with
elasticity and material properties Understand
2
a CAAE002.02 Describe the resistance and deformation in members
which are subjected to axial, flexural and torsion loads. Understand b CAAE002.03 Discuss thermal explanations in solid bars and induced
thermal stresses Understand
3
a CAAE002.04 Solve for bending and shear stresses of symmetric and
un-symmetric beams under loading conditions Remember b CAAE002.02 Describe the resistance and deformation in members
which are subjected to axial, flexural and torsion loads. Understand
4
a CAAE002.05 Calculate the shear stresses developed in various sections
of beams. Understand
b CAAE002.06 Calculate the flexural developed in various sections of
beams of real field problems. Understand
5
a CAAE002.08 Analyze the redundant complex structural components
subjected to different loading and boundary conditions. Remember b CAAE002.09 Solve for deflections of beams under loading with
various approaches Remember
6
a CAAE002.08 Analyze the redundant complex structural components
subjected to different loading and boundary conditions. Remember b CAAE002.10 Calculate the stability of structural elements and
determine buckling loads. Understand
7
a CAAE002.08 Analyze the redundant complex structural components
subjected to different loading and boundary conditions. Understand b CAAE002.09 Solve for deflections of beams under loading with
various approaches Remember
8
a CAAE002.09 Solve for deflections of beams under loading with
various approaches Remember
b CAAE002.09 Solve for deflections of beams under loading with
various approaches Remember
9
a CAAE002.13
Describe the behavior of structural components subjected to various loading and support conditions based on principles of equilibrium and constitutional relationships.
Understand
b CAAE002.14 Explain the stress transformation and concept of
principle plane and principle stresses Understand
10
a CAAE002.14 Explain the stress transformation and concept of
principle plane and principle stresses Understand b CAAE002.14 Explain the stress transformation and concept of
principle plane and principle stresses Understand
