JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II THEORY OF STRUCTURES Previous Question Paper (April/May - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
(25 Marks)
What do you mean by bar of uniform strength?
Answer
A bar of uniform strength is a structural member designed such that the intensity of stress remains constant throughout its entire length under the action of an axial load. This is achieved by varying the cross-sectional area of the bar in proportion to the axial force at any given section, ensuring that the material is utilized efficiently at its maximum allowable stress level.
What is the meaning of ‘strength of a section’?
Answer
The strength of a section refers to the maximum internal force or moment that a structural member can resist before it reaches its limit state, such as yielding, rupture, or buckling. It represents the load-carrying capacity of a specific cross-section based on its geometric properties, material characteristics, and the nature of the applied stress (e.g., axial, bending, shear, or torsion).
In design, this is typically calculated using the ultimate strength of the material and the section modulus or area. A section is considered adequate if its calculated strength exceeds the factored design forces imposed by the external loads.
What do you mean by end condition of a column? What are the important end conditions for a column?
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What is moment-area method? Where is it conveniently used?
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What is the stress function?
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Explain briefly the term ‘shear stress’ and ‘complementary stress’ with proper illustration.
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Show that for a rectangular section the maximum shear stress is 1.5 times the average stress.
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How will you justify that Rankin’s formula is applicable for all lengths of columns, ranging from short to long columns.
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Explain Clayperon’s method for statically indeterminate structures.
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What do you understand by an Airy’s stress function in two dimensions?
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Part B
(50 Marks)
An axial pull of 40 kN is acting on a bar consisting of three sections length 30 cm, 25 cm, and 20 cm and of diameters 2 cm, 4 cm and 5 cm respectively. If the Young’s modulus = 2 × 105 N/mm2, determine stress in each section and total extension of the bar.
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A cantilever 2m long is loaded with a uniformly distributed load of 2 kN/m over a length of 1m from the fixed end. It also carries a point load of 4 kN at distance of 0.5m from the free end. Draw the shear force and bending moment diagrams.
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Prove that the ratio of depth to width of the strongest beam that can be cut from a circular log of diameter d is 1.414. Hence calculate the depth and width of the strongest beam that can be cut of a cylindrical log of wood whose diameter is 300 mm.
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A beam of I-section is having overall depth as 500 mm and overall width as 190 mm. The thickness of flanges is 25 mm whereas the thickness of the web is 5 mm. The moment of inertia about N.A. is given as 6.45 × 108 mm4. If the section carries a shear force of 40 kN, calculate the maximum shear stress. Also sketch the shear stress distribution across of the section.
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A simply supported beam of length 4 m is subjected to uniformly distributed load of 30 kN/m over the whole span and deflects 15 mm at the centre. Determine the crippling loads when this beam is used as a column with the following conditions:
One end fixed and other end hinged
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Both the ends pin jointed.
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A hollow cylindrical cast iron column is 4 m long with both ends fixed. Determine the minimum diameter of the column if it has to carry a safe load of 250 kN with a factor of safety of 5. Take the internal diameter as 0.8 times the external diameter. Take σc = 550 N/mm2 and a = 1/1600 in Rankine’s formula.
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A continuous beam ABCD of length 15 m rests on four supports covering 3 equal spans and carries a uniformly distributed load of 1.5 kN/m length. Calculate the moments at the supports. The support A is fixed and the other three are Roller supports.
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Calculate the vertical deflection of the joint B and the horizontal movement of the support D in the truss shown in figure. The cross-sectional area of each member is 1800mm2 and Young’s modulus, E, for the material of the members is 200 000 N/mm2.
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Derive the strain equations for three mutually perpendicular planes in terms of displacement functions and deduce compatibility equations.
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A solid shaft of circular cross-section supports a torque of 50 kN-m and a bending moment of 25 kN-m. If the diameter of the shaft is 150 mm calculate the values of the principal stresses and their directions at a point on the surface of the shaft?
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