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The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of $10\: MPa$. If one unit on the $\sigma -\tau$ plane is $1\: MPa$, the Mohr's circle representation of the state-of-stress is given by a circle with a radius ... radius of $10$ units on the $\sigma -\tau$ plane a point on the $\tau$ axis at a distance of $10$ units from the origin
asked Feb 19, 2020 in Applied Mechanics and Design jothee 4.9k points
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The state of stress at a point in a component is represented by a Mohr’s circle of radius $100$ MPa centered at $200$ MPa on the thermal stress axis. On a plane passing through the same point, the normal stress is $260$ MPa. The magnitude of the shear stress on the same plane at the same point is _______ MPa
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then strain ... same specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compression of the material of the block is $300 \: MPa$ and it follows the Tresca (maximum shear stress) criterion. Assume ... $340 \: MPa$ (compressive) $340 \: MPa$ (tensile) $260 \: MPa$ (compressive) $260 \: MPa$ (tensile)
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$
asked Feb 9, 2019 in Applied Mechanics and Design Arjun 24.6k points
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A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure. The glue used at the interface fails is Criterion 1: the maximum normal stress exceeds $2.5$ MPa Criterion 2: the maximum ... fails only because of criterion $1$ fails only because of criterion $2$ fails because of both criterion $1$ and $2$ does not fail
asked Feb 17, 2018 in Applied Mechanics and Design Arjun 24.6k points
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The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is $10$ kPa, then the normal stress $\sigma_y$ (in kPa) is $9.45$ $18.88$ $37.78$ $75.50$
asked Feb 17, 2018 in Applied Mechanics and Design Arjun 24.6k points
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If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is $\dfrac{\sigma_1 +\sigma_3}{2} \\$ $\dfrac{\sigma_1 -\sigma_3}{2} \\ $ $\sqrt{\dfrac{\sigma_1 +\sigma_3}{2}} \\$ $\sqrt{\dfrac{\sigma_1 -\sigma_3}{2}}$
asked Feb 17, 2018 in Applied Mechanics and Design Arjun 24.6k points
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The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=-40$ MPa. For the material of the component, the tensile yield strength is $\sigma _{y}=200$ MPa. According to the maximum shear stress theory, the factor of safety is $1.67$ $2.00$ $3.60$ $4.00$
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum normal stress (in MPa) at that point is ________.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3), S(0, 3)$. The rectangle is subjected to uniform strains, $\varepsilon _{xx}=0.001, \varepsilon _{yy}=0.002,\gamma _{xy}=0.003$. The deformed length of the elongated diagonal, up to three decimal places is _______ units.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to Yield stress Proportional limit Maximum stress Fracture stress
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following von Mises' criterion, the yield stress is _________ MPa.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is _____________MPa.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E=200 \: GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L = 2 \: m$ and $\delta=0.001 \: m$, the Poisson’s ratio of the plate material is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Engineering strain of a mild steel sample is recorded as $0.100\%$. The true strain is $0.010\%$ $0.055\%$ $0.099\%$ $0.101\%$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $50$ $MPa$ and $150$ $MPa$, respectively. The endurance, yield, and the ultimate strengths of the material are $200$ $MPa$, $300$ $MPa$ and $400$ $MPa$, respectively. The factor of safety using modified Goodman criterion is $\dfrac{3}{2} \\$ $\dfrac{8}{5} \\$ $\dfrac{12}{7} \\$ $2$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 \: mm$. All joints are pin joints. The stress (in $Pa$) in the link $AB$ is ___________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends as shown in the figure. The shear modulus for the cylinder is $G$ and the Young’s modulus is $E$. The vertical deflection at point A is $PL^3/(\pi R^4G)$ $PL^3/(\pi R^4E)$ $2PL^3/(\pi R^4E)$ $4PL^3/(\pi R^4G)$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 strength point of view is a point on the circumference at location Y a point at the center at location Y a point on the circumference at location X a point at the center at location X
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is $0.25$ $0.50$ $1.0$ $2.0$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 $2.0$ $1.0$ $0.5$ $0$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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$(0.8,130)$. $'Q'$ is the yield point, $'R'$ is the UTS point and $'S'$ the fracture point. The toughness of the material (in $MJ/m^3$) is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 material is $200$ $MPa$. The factor of safety calculated using Tresca (maximum shear stress) theory is $n_T$ ... . Which one of the following relations is TRUE? $n_T=(\sqrt{3}/2)n_V$ $n_T=(\sqrt{3})n_V$ $n_T=n_V$ $n_V=(\sqrt{3})n_T$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 $E$, respectively. For the deflection at $C$ to be zero, the ratio $\displaystyle{\frac{P}{F}}$ is ____________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 $10$ $mm$. The magnitude of maximum in-plane shear stress (in $MPa$) is ________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 $0.20$ $250$ $MPa$ and $0.20$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ = stress and $\varepsilon$ = strain)?
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table. ... $P-3, Q-4, R-1, S-5,T-2, U-6$ $P-4, Q-1, R-5, S-2,T-3, U-6$
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Which one of following is NOT correct? Intermediate principal stress is ignored when applying the maximum principal stress theory The maximum shear stress theory gives the most accurate results amongst all the failure theories As per the maximum strain energy theory, ... As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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