Questions without answers in Mechanics of Materials

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$.The maximum shear stress developed in the wir...

A steel plate having yield strength of $550$ MPa , is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2 \sigma$. Using distortion energy theo...

A cantilever beam of length $L$ is subjected to a concentrated load $P$ and a moment $M$ as shown in the figure below. Neglecting the mass of the beam, which one of the f...

A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of $20 \mathrm{~mm} \times 45 \mat...

A cylindrical pressure vessel made of steel has diameter of $3$ m and wall thickness of $15$ mm. For steel, Young's modulus and Poisson's ratio are $210$ GPa and $0.3$, r...

A welded square plate of $1 \mathrm{~m} \times 1 \mathrm{~m}$ is subjected to biaxial stress of magnitude $6.5$ MPa and $25$ MPa , as shown in the figure below. The ratio...

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $(\varepsilon_{z z})$ is...

A simply supported beam of length $1 \: \text{m}$ is subjected to a uniformly distributed bending moment of $1 \: \text{N m}$ per $\text{m}$ throughout the length as show...

Two plates of thickness $10 \: mm$ each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below.If the...

​​​​Which of the following beam(s) is/are statically indeterminate?

A horizontal beam of length $1200 \mathrm{~mm}$ is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distribut...

A solid massless cylindrical member of $50 \mathrm{~mm}$ diameter is rigidly attached at one end, and is subjected to an axial force $P=100 \mathrm{kN}$ and a torque $T=6...

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha=60^{\circ}$ with the horizontal. The c...

A beam is undergoing pure bending as shown in the figure. The stress $(\sigma)$-strain $(\varepsilon)$ curve for the material is also given. The yield stress of the mater...

The principal stresses at a point $\mathrm{P}$ in a solid are $70 ~ \mathrm{MPa},-70 ~ \mathrm{MPa}$ and $0$. The yield stress of the material is $100 ~ \mathrm{MPa}$. Wh...

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by $0$.)$\text{M1}$$\...

A beam of length $L$ is loaded in the $x y-$ plane by a uniformly distributed load, and by a concentrated tip load parallel to the $z$-axis, as shown in the figure. The r...

The figure shows a thin-walled open-top cylindrical vessel of radius $r$ and wall thickness $t$. The vessel is held along the brim and contains a constant-density liquid ...

Cylindrical bars $\mathrm{P}$ and $\mathrm{Q}$ have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficie...

Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\si...

The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$.(Answer in integer)

A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \ma...

A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}...

Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen?Stress value where the str...

A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}...

A shaft $\text{AC}$ rotating at a constant speed carries a thin pulley of radius $r= 0.4\:m$ at the end $C$ which drives a belt. A motor is coupled at the end $A$ of the ...

A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\...

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the foll...

Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft?Enhancing surface finishShot peening of the shaftIncreasing r...

A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in ...