Strength of Materials (CE-305) - Important Questions

For an axially loaded prismatic rod, calculate stress, strain and axial deformation ($\delta = PL/AE$).

Explain Mohr's circle and how principal stresses, principal planes and maximum shear stresses are obtained from it.

Given normal stresses $\sigma_x, \sigma_y$ and shear stress $\tau$, determine the principal stresses, maximum shear stress, and location/orientation of principal planes.

Deduce the relationship between Modulus of Elasticity $E$ and Modulus of Rigidity $G$.

Calculate the extension of a stepped prismatic bar with different diameters over different lengths under axial pull.

Write a brief note on stress and strain and Mohr's circle.

What are principal planes and principal stresses and why are they important?

Derive an expression for thermal stress developed in a bar due to temperature change.

A point is subjected to a tensile stress of 250 MPa in the horizontal direction and another tensile stress of 100 MPa in the vertical direction. The point is also subjected to a simple shear stress of 25 MPa. Such that when it is associated with the major tensile stress, it tends to rotate the element in the clockwise direction what is the magnitude of the normal and shear stresses on a section inclined at an angle of 20°, with the major tensile stress.

Given Young's Modulus and Modulus of Rigidity, determine Poisson's ratio and Bulk modulus numerically.

Calculate the elongation of a uniformly tapering circular bar under axial load for given dimensions, load and $E$.

Write short notes on: Longitudinal and lateral strain

Draw the shear force and bending moment diagrams for the given beam loading and determine bending moment values.

For a simply supported rectangular beam under uniformly distributed load, determine the maximum bending stress for a given load or the allowable UDL for a given stress limit.

Explain and show that shear stress distribution across a rectangular beam section is parabolic with sketches.

Derive the differential relations between intensity of loading, shear force and bending moment ($dV/dx = -w$, $dM/dx = V$).

Find the shear force / support reaction at the left support for a simply supported beam with an eccentric point load.

Numerical calculation of shear stress in an I-section beam for a given shear force.

Write the assumptions made in the theory of simple bending.

Derive the general shear stress formula $\tau = VQ/It$ for a loaded beam from fundamentals.

Using equal failure bending stress, find the UDL causing failure of a cantilever beam from the central failure load of a simply supported beam.

Write short notes on: Section Modulus, Point of Contra-flexure, Thermal Stresses, and Comparison of hollow and solid shafts.

Explain shear stress distribution across rectangular and circular sections.

Derive the expression for shear stress distribution over an I-section.

State and explain Mohr's first and second moment-area theorems for slope and deflection.

Find the free end deflection of a cantilever beam of length $L$ carrying a uniformly distributed load of intensity $W$ using Macaulay's method.

Using the double integration method, determine slopes at supports and maximum deflection for a simply supported beam of span $L$ carrying uniformly distributed load $w$ over the entire span.

Explain Macaulay's method for finding slope and deflection of beams.

Explain strain energy method and Castigliano's theorem.

Using Macaulay's method, for a simply supported beam of span $l$ carrying a concentrated load $W$ at distance $a$ from the left support, find slopes at supports, deflection under the load and maximum deflection.

A Load of $175\text{ N}$ falls through a height of $40\text{ mm}$ on to a collar rigidly attached to the lower end of a vertical bar $1.8\text{ m}$ long and of $1.8\text{ cm}^2$ cross-sectional area. The upper end of the vertical bar is fixed. Determine the maximum instantaneous stress induced in the bar. $E = 2 \times 10^5\text{ N/mm}^2$

Using the method of integration, determine slopes at supports and mid-span deflection for a simply supported beam of span $L$ with a concentrated load $P$ at $0.3L$ from the left support.

Determine slope and deflection of a simply supported beam of span L carrying a central point load P and a uniformly distributed load w over the entire span using the moment-area method.

Explain Rankine's formula for intermediate columns, including its basis and limitations.

Calculate the Euler crippling load (and safe load) for a strut/column of given section, length and end conditions.

Explain theories of failure (e.g., any three theories) with graphical representation / short notes on theories of failure

How much additional water must be pumped into a thin spherical vessel filled with water to reach a given internal pressure, accounting for vessel expansion and water compressibility?

Using Rankine's formula, determine the external and internal diameters of a hollow circular column with given length, end conditions, axial load, crushing stress, Rankine constant and factor of safety.

Explain the middle third rule and combined bending and torsion.

Derive Euler's formula for long columns with different end conditions.

State Euler's assumptions in column theory and explain the middle third rule.

A compound cylinder is made by shrinking a cylindrical of external diameter $300\text{ mm}$ and internal diameter of $250\text{ mm}$ over another cylindrical of external diameter $250\text{ mm}$ and internal diameter $200\text{ mm}$. The radial pressure at the junction after shrinking is $8\text{ N/mm}^2$. Find the final stresses sent up across the section, when the compound cylinder is subjected to an internal fluid pressure of $84.5\text{ N/mm}^2$.

Derive an expression for circumferential stress for a thin spherical shell of internal diameter $d$, wall thickness $t$ and subjected to an internal pressure $p$.

Given an additional volume of fluid pumped into a thin cylindrical shell filled with fluid, find the resulting fluid pressure and induced hoop stress.

Calculate Euler's critical load for a given hollow column and compare it with Rankine's critical load, and find the length at which both formulas give equal critical load.

Determine inside and outside diameters of a hollow shaft to transmit required torque/power satisfying both allowable shear stress (strength) and allowable angle of twist (stiffness).

Determine the required/minimum diameter of a solid shaft to transmit a given torque or power at given speed without exceeding allowable shear stress.

Explain pure torsion and derive the torsion equation, stating the assumptions made.

Find the maximum shear stress induced in a hollow circular shaft of given dimensions transmitting a given torque.

Explain torsion of a hollow circular shaft and compare its strength and stiffness with a solid shaft.

Derive the expression for angle of twist of a circular cross-section member subjected to torsional moment.

Determine the required length of a wire of given diameter to allow a given angle of twist without exceeding allowable shear stress.

Determine the required diameter of a solid shaft to transmit a given power at a given speed without exceeding allowable shear stress.

Explain the principle of super position.