Recent questions tagged mechanics-of-materials

A machine element XY, fixed at end X, is subjected to an axial load P, transverse load F, and a twisting moment T at its free end Y. The most critical point from the stre...

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is$0.25$$0.50...

A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is$2.0$$1.0$$0.5$$0$

A $300$ $mm$ thick slab is being cold rolled using roll of $600$ $mm$ diameter. If the coefficient of friction is $0.08$, the maximum possible reduction (in $mm$) is ____...

A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical r...

A hypothetical engineering stress-strain curve shown in the figure has three straight lines $PQ, QR, RS$ with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,...

The principal stresses at a point inside a solid object are $\sigma _1$ = $100$ $MPa$, $\sigma _2$ = $100$ $MPa$ and $\sigma _3$ = $0$ $MPa$. The yield strength of the ma...

A simply-supported beam of length $3L$ is subjected to the loading shown in the figure.It is given that $P=1\: N$, $L=1\:m$ and Young’s modulus $E=200\:GPa$. The cross-se...

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respect...

A cantilever beam having square cross-section of side $a$ is subjected to an end load. If $a$ is increased by $19\%$, the tip deflection decreases approximately by$19\%$$...

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that $r_3>r_1$ and $r_4 r_2$, and that the are...

A rigid ball of weight $100$ $N$ is suspended with the help of a string. The ball is pulled by a horizontal force $F$ such that the string makes an angle of $30^o$ with t...

The dimensions of a cylindrical side riser (height = diameter) for a $25 \: cm \times 15 \: cm \times 5 \: cm$ steel casting are to be determined. For the tabulated shape...

A shaft of length $90 \: mm$ has a tapered portion of length $55 \: mm$. The diameter of the taper is $80 \: mm$ at one end and $65 \: mm$ at the other. If the taper is m...

A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) is ________

A weight of $500$ $N$ is supported by two metallic ropes as shown in the figure. The values of tensions $T_1$ and $T_2$ are respectively$433$ $N$ and $250$ $N$$250$ $N$ a...

A cylindrical tank with closed ends is filled with compressed air at a pressure of $500$ $kPa$. The inner radius of the tank is $2$ $m$, and it has wall thickness of $10$...

The strain hardening exponent $n$ of stainless steel SS $304$ with distinct yield and UTS values undergoing plastic deformation is$n < 0$$n = 0$$0 < n < 1$$n = 1$

For the given fluctuating fatigue load, the values of stress amplitude and stress ratio are respectively$100$ $MPa$ and $5$$250$ $MPa$ and $5$$100$ $MPa$ and $0.20$$250$ ...

A hollow shaft ($d_o$ = $2d_i$ where $d_o$ and $d_i$ are the outer and inner diameters respectively) needs to transmit $20$ $kW$ power at $3000$ $RPM$. If the maximum per...

A hollow shaft of $1 \: m$ length is designed to transmit a power of $30\: kW$ at $700 \text{rpm}$. The maximum permissible angle of twist in the shaft is $1^{\circ}$. Th...

In a plane stress condition, the components of stress at a point are $\sigma_x =20$ $MPa$, $\sigma _y=80$ $MPa$ and $\tau_ {xy}$=$40$ $MPa$ The maximum shear stress (in $...

A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus of...

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bend...

A rope-brake dynamometer attached to the crank shaft of an $I.C$. engine measures a brake power of $10$ $kW$ when the speed of rotation of the shaft is $400$ $rad/s$. The...

The uniaxial yield stress of a material is $300$ $MPa$. According to von Mises criterion, the shear yield stress (in $MPa$) of the material is _______

A gas is stored in a cylindrical tank of inner radius $7$ $m$ and wall thickness $50$ $mm$. The gage pressure of the gas is $2$ $MPa$. The maximum shear stress (in $MPa$)...

A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is $200$ $MPa$, the change in the strain is $0.001$. If the Poisson’s ra...