Recent questions tagged 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 rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is $l$ and the fillet weld...

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...

In a deep drawing operation of a rectangular sheet metal, $30\%$ stretching in length results in $15\%$ reduction in thickness. Assuming volume constancy, the normal anis...

A block of mass $1 \: kg$ connected to a spring of stiffness $10 \mathrm{~N} \mathrm{~m}^{-1}$ is operating in a viscous medium such that the damping ratio (or damping fa...

​​​​​The system shown in the figure below consists of a cantilever beam (with flexural rigidity $E I$ and negligible mass), a spring (with spring constant $K$ and negligi...

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 one of the following failure theories is the most conservative design approach against fatigue failure?Soderberg lineModified Goodman lineGerber lineYield line

​​​​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}$$\...

The figure shows a block of mass $m=20 \mathrm{~kg}$ attached to a pair of identical linear springs, each having a spring constant $k=1000 \mathrm{~N} / \mathrm{m}$. The ...

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 ...