Q1:

A steel wire of 20 mm diameter is bent into a circular shape of 10m radius. If E, the modulus of elasticity is 2 × 10⁶ kg/cm² then the maximum stress induced in the wire is

Q2:

Consider the following statements:

1. If a beam has two axes of symmetry even then shear centre does not coincide with the centroid

2. For a section having one axis of symmetry, the shear centre does not coincide with the centroid but lies on the axis of symmetry.

3. If a load passes through the shear centre, then there will be only bending in the cross-section and no twisting.

Which of these statements are correct?

Q3:

A ratio of moment carrying capacity of a circular beam of diameter D and square beam of size ‘D’ is

Q4:

A circular shaft of diameter ‘D’ is made of a material for which Young’s Modulus of Elasticity is ‘E’ and Poisson’s Ratio is ‘V’. The ratio of flexural rigidity to torsional rigidity for the sift is

Q5:

Which of the following statements are correct?

1. Strain in the direction of applied stress is known as longitudinal strain.

2. Tensile stress results in tensile strain in linear and lateral directions.

3. Strains in all directions perpendicular to the applied stress are volume to original volume is known as volumetric strain.

Q6:

The longitudinal strain of cylindrical bar of 25 mm diameter and 1.5m length is found to be 3 times its lateral strain in a tensile test. What is the value of Bulk Modulus by assuming E = 1 × 10⁵ N/mm²?

Q7:

For an elastic material, Poisson’s ratio is µ, Modulus of Elasticity is E, Modulus of Rigidity is C and Bulk Modulus is K. µ is expressible in terms of K and C as

Q8:

A mild steel bar of length 450 mm tapers uniformly. The diameters at the ends are 36 mm and 18 mm, respectively. An axial load of 12 kN is applied on the bar. E = 2 × 10⁵ N/mm². The elongation of the bar will be

Q9:

What is the stress at the section x – x for the bar ABCD with uniform cross- section 1000 mm²?

Q10:

What is the horizontal deflection of free end C in the frame shown below.

Q11:

Match list-I with List-II and select the correct answer using the codes given below the lists-

List-I	List-II
A. Partial derivative of total strain energy with respect to load.	1. Expression for shear force
B. Derivative of deflection	2. Expression for slope
C. Derivative of slope	3. Expression for bending moment
D. Derivative of moment.	4. Deflection under the load

 

Q12:

The strain energy stored in simply supported beam of span “L” and flexural rigidity EI carrying a central concentrated load W is-

Q13:

Match List-I (Real beam) with List-II (Conjugate beam) on the basis of analogy and select the correct answer.

List-I	List-I
A. Curvature	1. Shear
B. Deflection	2. Load
C. Slope	3. Moment

 

Q14:

A beam has a triangular cross-section, having base ‘b’ and altitude ‘h’. If a section of the beam is subjected to a shear force F, the shear stress at the level of neutral axis in the cross-section is given by

Q15:

The shear centre of a section is defined as that point

Q16:

Two spring of stiffness $K_A{\text{ and K}}_B$are placed one inside the other so as to compress by the same amount under the applied axial load. The combined stiffness of the two springs will be-

Q17:

A close - coiled helical spring has 100 mm mean diameter is made of 20 turns of 10 mm diameter steel wire. The spring carries an axial load of 100 N , modulus of rigidity is 84 G Pa, The shearing stress developed in the spring in N/ mm² is

Q18:

When two springs are in series, the stiffness of the composite spring will be

Q19:

Consider the following statements-

1. The deflection of a closed helical spring due to an axial load is inversely proportional to the modulus of rigidity of the spring material.

2. The stiffness of a closed helical spring with axial load is directly proportional to the modulus of rigidity of the spring material.

3. The stiffness of a closed helical spring with axial of spring type of these statements.

Q20:

A solid shaft of 80mm diameter is transmitting 100 KW of power at 200 rpm. The maximum shear stress induced in the shaft will nearly be-

Q21:

A solid circular shaft has a diameter d. Its polar modulus will be

Q22:

1. The shear stress distribution across the section of a circular shaft subjected to twisting varies parabolically.

2. The shear stress at the center of a circular shaft under twisting moment is zero.

3. The shear stress at the extreme fibers of a circular shaft under twisting moment  is zero.

Which of the above statement (s) is/are correct?

Q23:

If the shear force diagram of a simply supported beam is parabolic, then the load on the beam is

Q24:

Neglecting self wt. which of the following beams will have points of contra flexure?

Q25:

A loaded beam PQRS is shown in the given figure.

The magnitude of support reaction at R will be zero if the value of Load “W” is

Q26:

A simply supported beam AB of span L carries two concentrated loads “W” each at point “L/3” from A and B. What is the shear force in the middle one-third portion of the beam?

Q27:

A thin cylindrical shell made of mild steel plate is 1000 mm in diameter. It is to be subjected to an internal pressure of 2N/$m{m}^2$. If the material yields at 200 N/mm², the thickness of the plate in mm on the basis of Rankin’s theory of failure ( assuming a factor of safety of 3) would be

Q28:

A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m². The maximum circumferential stress in the cylinder will occur at a radius of   

Q29:

A seamless pipe with 80 cm diameter carries a fluid under a pressure of 2N/mm². If the permissible tensile stress is 100N/ mm², the minimum required thickness of the pipe is

Q30:

A thin cylindrical shell of diameter “d” and length “l” and thickness “t” is subjected to an internal pressure “P”. What is the ratio of longitudinal strain to hoop strain in terms of poison’s ratio $\text{'}\text{'}\mu \text{'}\text{'}$.

Q31:

Consider the following statements:

For a component made of ductile material, the failure criterion will be

1. endurance limit, if the external force is fluctuating

2. fatigue, if the external force is fluctuating

3. yield stress, if the external force is static

Which of the above statements are correct?

Q32:

Consider the following :

The parallel fillet welded joint is designed for

1. Tensile strength

2. Compressive strength

3. Bending strength

4. Shear strength

Which of the above is/are correct?

Q33:

How can shock absorbing capacity of a bolt be increased

Q34:

In a fillet welded joint, the weakest area of the weld is

Q35:

A rope has been designted as 6 × 19. The numbers 6 and 19 respectively stand for

Q36:

If the principal stresses and maximum shearing stresses are of equal  value at a point in a stressed body, the state of stress can be termed as

Q37:

Statement (I) : Mohr’s circle of stress can be related to Mohr’s circle of strain by some constant of proportionality.

Statement (II) : The relationship is a function of yield strength of the material.

Q38:

If E = elasticity modulus, I = moment of inertia about the neutral axis and M = bending moment in pure bending under the symmetric loading of a beam, the radius of curvature of the beam :

1. increases with E

2. increases with M

3. Decreases with I

4. Decreases with M

Which of these are correct?

Q39:

For the two shafts connected in parallel

Q40:

The equivalent bending moment under combined action of bending moment M and torque T is