# Recent questions tagged deflection-of-beams

The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).
The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).
Endurance limit of a beam subjected to pure bending decreases with decrease in the surface roughness and decrease in the size of the beam increase in the surface roughness and decrease in the size of the beam increase in the surface roughness and increase in the size of the beam decrease in the surface roughness and increase in the size of the beam
A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, and area moment of inertia $I$, the magnitude of the maximum deflection is $\dfrac{qL^4}{15EI} \\$ $\dfrac{qL^4}{30EI} \\$ $\dfrac{qL^4}{10EI} \\$ $\dfrac{qL^4}{60EI}$
A horizontal cantilever beam of circular cross-section, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cdot m$ at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a circle of mean radius $R$. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is _____ $MPa$.
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.
A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the Young's modulus is $E$. The magnitude of the maximum deflection is $\dfrac{ML^2}{2EI} \\$ $\dfrac{ML^2}{EI} \\$ $\dfrac{2ML^2}{EI} \\$ $\dfrac{4ML^2}{EI}$
A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for steel, the critical axial load (in kN) is ______ (correct to two decimal places).
The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is $\dfrac{P^{2}L^{3}}{6EI} \\$ $\dfrac{P^{2}L^{3}}{3EI} \\$ $\dfrac{PL^{3}}{3EI} \\$ $\dfrac{PL^{3}}{6EI}$
Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is $\dfrac{d}{2} \\$ $\dfrac{\pi d}{2} \\$ $d \\$ $\pi d$
A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the right end is $\dfrac{wL}{2} \\$ $\dfrac{3wL}{8} \\$ $\dfrac{wL}{4} \\$ $\dfrac{wL}{8}$
A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is given by $w=\dfrac{-Mx}{12EIL}(L-x)(x+c)$ where $E$ is the Young's modulus, $I$ is the area moment of inertia ... $x$ = $0$ is $ML/(2EI)$ $ML/(3EI)$ $ML/(6EI)$ $ML/(12EI)$
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-section is a square with dimension $10\:mm\times10\:mm$. The bending stress ... beam at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
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 $19\%$ $29\%$ $41\%$ $50\%$
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 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 elasticity of the material of the beam is $210 \: GPa$. The magnitude of slope (in radian) at $Q$ ($20 \: mm$ from the fixed end) is ________
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 bending moment (in $kN$-$m$) at fixed end O is $2.5$ $5$ $10$ $25$
A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______
Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degrees) is __________
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$
Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$
A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertical deflection of the beam is given by $\dfrac{wL^4}{8EI} \\$ $\dfrac{wL^4}{16EI} \\$ $\dfrac{wL^4}{4EI} \\$ $\dfrac{wL^4}{24EI}$
The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are applied at the free end of the beam then the value of the slope at the free end is $\dfrac{1}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{PL^2}{EI} \\$ $\dfrac{3}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{5}{2}\dfrac{PL^2}{EI}$
Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $0.01$ $m$. The frequency of vibration of the beam, with a $0.5$ $kg$ mass attached at the free tip, is $100$ $Hz$. The flexural rigidity (in $N$.$m^2$) of the beam is _______
A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in $N$ at the left support is $\text{zero}$ $L/3\pi$ $L/\pi$ $2L/\pi$
A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is $\text{zero}$ $W/4$ $W/2$ $W$