AMIE Study Circle Blog

A stepped circular bar 150 mm long with diameters 20, 15, and 10 mm along length AB = 40 mm, BC - 45 mm, and CD = 65 mm, respectively is subjected to various forces as shown in Fig. P-14.12(a). Determine the change in its length if E = 200 \(kN/m{m^2}\). (AMIE Winter 2023) Solution Considering portion AB, a tensile force of 20 kN is to act to maintain equilibrium. For portion BC, if it is considered to be subjected to a tensile force of 5 kN, then the net force at section B will be 15 kN as shown. Similarly, for the portion CD, a compressive force of 10 kN would make a net force of 15 kN at section C. Area of cross sections \(\begin{array}{l}{A_1} = \frac{\pi }{4}{(20)^2} = 314.16\,m{m^2}\\{A_2} = \frac{\pi }{4}{(15)^2} = 176.7\,m{m^2}\\{A_3} = \frac{\pi }{4}{(10)^2} = 78.54\,m{m^2}\end{array}\) Extension of AB \(\begin{array}{l}\delta {L_1} = \frac{{20x40}}{{314.16E}}\\ = \frac{{20x40}}{{314.16x200}}\\ = 1.273x{10^{ - 2}}\,mm\end{array}\) Extension of BC \(\begin{array}{l}\delta {L_2}...

Answer the following questions in brief (10 x 2) State the difference between thin and thick cylinder.  Thin cylinder The cylinder which has a thickness is less than 1/10 to 1/20 of its diameter, that cylinder is called a thin cylinder. A cylinder whose wall thickness is less than 1/20 times of its internal diameter The thin cylinder is only resisted by internal pressure. Low stress consuming capacity. Thick cylinder The cylinder which has a thickness is more than 1/20 of its diameter that cylinder is called a thick Cylinder. A cylinder whose wall thickness is greater than 1/20 times its internal diameter. The thick cylinder is resisted by internal as well as external pressure. More stress consuming capacity. What are sagging and hogging bending moments? The bending moment at a section is considered positive if the bending moment at that section is such that it tends to bend the beam to a curvature having concavity at the top. Similarly the bending moment (B.M.) at a section is con...

Write short notes on (4 marks each) Generalised Hooke’s law Hooke’s Law states that when a material is loaded within the elastic limit, the stress is proportional to the strain produced by the stress. This means the ratio of the stress to the corresponding strain is a constant within the elastic limit. This constant is known as Modulus of Elasticity or Modulus of Rigidity or Elastic Modulii. Differential equation of equilibrium The Small-Strain Stress-Strain Relations Simple Shear   Pure shear   Tresca yield criteria According to this theory, the failure of material will occur when the maximum shear stress in a material reaches the value of maximum shear stress in simple tension at the elastic limit. The maximum shear stress in the material is equal to half the difference between the maximum and minimum principal stress. If σ₁, σ₂ and σ₃ are principal stresses at a point in material for wh ich σ t * i s the principal stress in simple tension at the elastic limit, the...

Choose the correct answer in the following questions (10 x 2) 1. There is always a limiting value of load up to which strain is totally disappeared on the removal of load, the stress corresponding to this load is called as: (a) Elastic limit (b) Unit stress (c) Yield stress (d) Ultimate stress 2. In a two-dimensional stress system the maximum shear stress occurs on planes inclined with horizontal as: (a)  (b)  (c) 90⁰ (d) 0° 3. In a cantilever beam with a uniformly distributed load, the shear force varies as (a) linear laws (b) parabolic law (c) cubic law (d) constant, does not vary 4. The diameter of the kernel of a circular section (no tension) is (a) d/2 (b) d/3 (c) d/4 (d) d/√2 5. The amount of deflection of a beam subject to some type of loading depends on : (a) cross section (b) bending moment (c) either (a) or (b) (d) both (a) and (b) 6. A pipe of 200 mm internal diameter and 50 mm thickness carriers a fluid at a pressure of 5 MN/m². The maximum circumferential stress w...

Explain the following in brief  (2 marks each) Free body diagram. In many problems, it is essential to isolate the body under consideration from the other bodies in contact and draw all the forces acting on the body. For this, first, the body is drawn and then applied forces, self-weight and the reactions at the points of contact with other bodies are drawn. Such a diagram of the body in which the body under consideration is freed from all the contact surfaces and shows all the forces acting on it (including reactions at contact surfaces), is called a Free Body Diagram (FBD). Relationship between elastic constants. Where, K is the Bulk modulus G is the shear modulus or modulus of rigidity. E is Young’s modulus or modulus of Elasticity. Unit of Modulus of elasticity E is N/m² or Pascal. Point of contra flexure in beams. Point of Contraflexure.  It is the point where the B.M. is zero after changing its sign from positive to negative or vice versa. Mohr’s circle. Mohr’s circle i...

1. In the tension test the specimen is subjected to tensile load. The maximum shear stress occurs at an angle with the axis of the specimen (a) 45° (b) 60° (c) 90° (d) 180° 2. The fatigue failure of the specimen occurs most importantly due to (a) High value of alternating stress (b) A large number of cycles (c) Propagation of internal crack (d) None of the above 3. Total elongation produced in a bar due to its self-weight is given by (a) gρl 2 /E (b) gρl 2 /2E (c) gpl/E (d) gpl/2E 4. Which of the following is the statically indeterminate structure (a) Cantilever beam (b) Simply supported beam (c) Fixed-beam (d) None of the above 5. The strength of the beam mainly depends on (a) Bending moment (b) C. G of the section (c) Section Modulus (d) Weight 6. In a thick cylinder subjected to internal pressure the radial stress at the outer surface is (a) Always more than zero (b) Always less than zero (c) Usually equal to zero (d) None of the above 7. In the case of a hollow shaft the a...