Recent questions and 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...