Strength of Material (ME-304) - Important Questions

Two or more dissimilar bars in parallel share an axial load with equal deformation; find stress in each bar given loads, areas/lengths and elastic moduli.

Draw and explain the stress-strain diagram for mild steel.

Determine strain energy stored in an axially loaded bar under gradual tensile load given length, diameter, load and $E$.

From tensile test elongation and torsion test angle of twist data, evaluate Poisson's ratio and the three elastic moduli ($E$, $G$, $K$).

Determine the maximum axial load $P$ for a three-segment steel-aluminum-bronze bar from allowable stresses (and overall axial deformation limit where given).

Derive the expression for elongation of a uniformly tapering circular bar of end diameters $D$ and $d$ subjected to axial load $P$.

What are principal planes and principal stresses, and what is Mohr's stress circle and its use in stress analysis?

For a material under two perpendicular tensile stresses, determine the plane of maximum obliquity and the resultant stress on that plane.

Define volumetric strain and prove that it equals the algebraic sum of three mutually perpendicular linear strains

A square bar of $25\text{ mm}$ side is held between two rigid plates and loaded by an axial pull equal to $300\text{ kN}$ as shown in figure. Determine the reactions at end A and C and elongation of the portion AB. Take $E = 2 \times 10^5\text{ N/mm}^2$.

Determine shaft diameter under combined bending and twisting moment using maximum principal stress and maximum shear stress theories.

Write short notes on Shear Modulus, Mohr's Circle, Composite Beams and Quarter-Fourth Rule.

A simply supported beam fails under a central point load; using the same failure stress, find the uniformly distributed load that causes failure of a cantilever beam of given size.

Describe the bending of composite sections and derive the expression for bending stress.

Draw shear force and bending moment diagrams for the given cantilever beam.

Explain the concept of deflection of beams and list factors affecting deflection.

Determine the deflection (maximum / free-end) of a cantilever beam under point loading.

Derive the differential relationships between load intensity $w$, shear force $S$ and bending moment $M$ in a beam, and define point of contraflexure.

Explain the moment-area method for determining slope and deflection of beams.

What is Macaulay's method for beam deflection and its advantages over direct integration?

Numerical problem to find load for zero deflection at a point given $E$ and $I$.

Find free-end deflection of a cantilever of length $L$ with point load $W$ using Macaulay's method.

For a simply supported beam with UDL plus central point load, find magnitude and location of peak bending moment and design rectangular section for allowable stress.

Derive the shear stress distribution for a circular cross-section and plot the distribution.

Derive the torsion equation $T/J = \tau/r = G\theta/L$ for a circular shaft under torsion, stating assumptions.

Explain the advantages of hollow shafts over solid shafts for power transmission.

Compare the weights of equal-length solid and hollow shafts transmitting the same torque at the same maximum shear stress for a given diameter ratio.

Determine maximum/minimum shearing stress in a hollow shaft and required diameter of solid shafts for given loading and allowable stress.

Prove a hollow shaft of equal weight and material resists more torque than a solid shaft, and state for which materials maximum principal stress theory is suitable.

For a stepped circular shaft with specified angles of twist at sections A, C, D, determine the applied torques, the angle of twist at section B, and the maximum shear stress in each segment.

Deduce expressions for maximum shear stress/torque in solid and hollow circular shafts.

Calculate maximum torque limited by both angle of twist and allowable shear stress.

Determine diameter of bolt subjected to axial pull and transverse shear force using theories of failure

Derive the expression for distortion energy per unit volume under principal stresses $\sigma_a, \sigma_b, \sigma_c$ and obtain the Von Mises failure condition.

Write short notes on any two of: Column and strut, Maximum Shear Strain Theory, Elastic curve of a beam, Hooke's law.

Discuss selection of appropriate failure theories for different materials and loading conditions

Explain theories of failure for ductile materials and brittle materials

Discuss / explain / list the different theories of failure

Determine factor of safety or principal stresses using maximum shear stress theory for given biaxial principal stresses

Explain the Maximum Distortion Energy Theory (Von Mises theory) for failure under complex loading, including its application to ductile vs brittle materials and limitations.

Determine torque T for yielding of solid shaft under axial compressive load P and torque T using maximum shear stress and maximum distortion energy criteria

Explain any three theories of failure along with their graphical representation.

Determine diameter of shaft subjected to combined bending moment and torque using theories of failure

Calculate thickness of thin cylindrical shell under internal pressure using maximum principal stress, maximum shear stress and maximum shear strain energy theories

What is slenderness ratio and its significance for column behaviour?

Derive Rankine's formula for columns and explain the significance of the constants used.

Determine minimum / shortest length at which Euler's formula is applicable and safe central load

Calculate Euler's buckling / crippling load or safe load for a column of given section, length and end condition

What is equivalent / effective length of a column and its values / use for different end conditions?

Determine safe central load for a strut with different effective lengths about different centroidal axes

Derive Euler's crippling load for a long column with both ends pin-jointed / hinged

Compare Rankine's and Euler's crippling loads for a given pin-ended tubular strut and find the limiting length for validity of Euler's formula.

Define crippling load and give the effective length of a column for both ends hinged and both ends fixed end conditions.

State assumptions of Euler's theory for long columns, including when to use Rankine's formula instead

Derive Euler's crippling load for a long column with both ends fixed