A thin uniform circular strip, flexural rigidity EI, fixed at C and is free to slide...
A thin uniform circular strip, flexural rigidity EI, fixed at C and is free to slide without friction at A. The strip carries a vertical force F at B as shown. Determine the horizontal reaction at A using Castigliano’s theorem. Answer.411F
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A thin uniform circular strip, flexural rigidity EI, fixed at C
and is free to slide...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load,...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load, Pz(x), as shown below: a) Find the deflection w(x) (10pts) b) Sketch the shear force V(x) and the beading moment M(x) along the length of the beam, labeling all significant points. (5pts) c) Calculate the maximum bending stress, Omax, and indicate where it occurs. (5pts) z, W Cross Section - 1/3 — * - 2/3 —
The continuous beam ABCD shown in Figure Q2(a) has a flexural rigidity EI = 1000 kNm2....
The continuous beam ABCD shown in Figure Q2(a) has a flexural
rigidity EI = 1000 kNm2. The beam is subjected to a concentrated
load at point B and a uniform load from points C to D.
(b) The beam ABCD shown in Figure Q2(b) is identical to that in Figure Q2(a), except that the roller support at point is replaced by a linear spring of stiffness K = 500 kN/m and point D settles (downwards) by 6 cm, calculate the...
By stiffness method : determine the displacements at Joint B and at Joint C in the three-span beam shown in the figure below. The flexural rigidity of the beam is EI and is constant along the length o...
By stiffness method : determine the displacements at Joint B and
at Joint C in the three-span beam shown in the figure below. The
flexural rigidity of the beam is EI and is constant along the
length of the beam. Note that L1 = L2 = L3 = L P1 = P2 = P3 = P
M = PL
wL = P Also, find the reactions at Joint A.
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い12 8
The cantilevered beam shown here has a known rigidity, EI, andlength, b, and is loaded...
The cantilevered beam shown here has a known rigidity, EI, and
length, b, and is loaded with a point force and a point moment as
shown a) Determine all reactions forces and draw the shear and
moment diagrams for this loading.b) Using discontinuity functions and the integration method,
find the deflection and the slope of the beam at the free
end.c) Using the moment-area method, find the deflection and the
slope of the beam at the location of the point load.
A small bead of mass m can slide without friction on a circular hoop that is...
A small bead of mass m can slide without friction on a circular hoop that is in a vertical plane and has a radius R. The hoop rotates at a constant angular velocity ω about a vertical axis through the diameter of the hoop. Our goal is to find the angle β, as shown, such that the bead is in vertical equilibrium. We break the problem into several steps. a) Assume the bead is in vertical equilibrium and does not...
1. The ends of a uniform bar AB with length l= 36.0 in and weight W...
1. The ends of a uniform bar AB with length l= 36.0 in and weight W = 30.0 lb are attached to collars of negligible weight that slide without friction along fixed bars. A vertical force P is applied to collar B. The bar is initially at rest in the position shown and the initial angular acceleration of A is 40.0 ft/s to the left, aA = – 40 ft/s i. o= 30° {= 36 in O Draw a free...
A conducting rod of mass m and negligible resistance is free to slide without friction along...
A conducting rod of mass m and negligible resistance is free to slide without friction along two parallel rails of negligible resistance separated by a distance I and connected by a resistor R. The rails are attached to a long inclined plane that makes an angle with the horizontal. There is a magnetic field B as shown. (a) Show that there is a retarding force on the bar and find an expression for this force. (b) Find an expression for...
A small bead of mass m is free to slide along a long, thin, frictionless rod,...
A small bead of mass m is free to slide along a long, thin, frictionless rod, which spins in a horizontal plane abut one end at a frequency of f (i.e., f revolutions per second). Show that the displacement of the bead from the center of rotation as a function of time t is given by r(t) = A exp(ct) + B exp(–Ct). Find the expression for the constant C. Also, how would you determine A and B?
11. A uniform thin rod of length L and mass M, pivoted at one end as...
11. A uniform thin rod of length L and mass M, pivoted at one end as shown above, is held horizontal and then released from rest. Ignore all effects due to friction. (a) Find the angular speed of the rod as it sweeps through the vertical position. solution: 、13g / L (b) Find the force exerted on the rod by the pivot at this instant. solution Mg (c) Starting from the horizontal position, what initial angular speed would be needed...
A small 4-lb collar C can slide freely on a thin ring of weight 6 lb...
A small 4-lb collar C can slide freely on a thin ring of weight
6 lb and radius 10 in. The ring is welded to a short vertical
shaft, which can rotate freely in a fixed bearing. Initially the
ring has an angular velocity of 35 rad/s and the collar is at the
top of the ring (θ = 0) when it is given a slight nudge. Neglecting
the effect of friction, determine a) the angular velocity of the
ring...
2. A beam with a uniform flexural rigidity, EI, is loaded by a triangular distributed load, Pz(x), as shown below: a) Find the deflection w(x) (10pts) b) Sketch the shear force V(x) and the beading moment M(x) along the length of the beam, labeling all significant points. (5pts) c) Calculate the maximum bending stress, Omax, and indicate where it occurs. (5pts) z, W Cross Section - 1/3 — * - 2/3 —
The continuous beam ABCD shown in Figure Q2(a) has a flexural
rigidity EI = 1000 kNm2. The beam is subjected to a concentrated
load at point B and a uniform load from points C to D.
(b) The beam ABCD shown in Figure Q2(b) is identical to that in Figure Q2(a), except that the roller support at point is replaced by a linear spring of stiffness K = 500 kN/m and point D settles (downwards) by 6 cm, calculate the...
By stiffness method : determine the displacements at Joint B and
at Joint C in the three-span beam shown in the figure below. The
flexural rigidity of the beam is EI and is constant along the
length of the beam. Note that L1 = L2 = L3 = L P1 = P2 = P3 = P
M = PL
wL = P Also, find the reactions at Joint A.
い12 8
い12 8
1. The ends of a uniform bar AB with length l= 36.0 in and weight W = 30.0 lb are attached to collars of negligible weight that slide without friction along fixed bars. A vertical force P is applied to collar B. The bar is initially at rest in the position shown and the initial angular acceleration of A is 40.0 ft/s to the left, aA = – 40 ft/s i. o= 30° {= 36 in O Draw a free...
A conducting rod of mass m and negligible resistance is free to slide without friction along two parallel rails of negligible resistance separated by a distance I and connected by a resistor R. The rails are attached to a long inclined plane that makes an angle with the horizontal. There is a magnetic field B as shown. (a) Show that there is a retarding force on the bar and find an expression for this force. (b) Find an expression for...
11. A uniform thin rod of length L and mass M, pivoted at one end as shown above, is held horizontal and then released from rest. Ignore all effects due to friction. (a) Find the angular speed of the rod as it sweeps through the vertical position. solution: 、13g / L (b) Find the force exerted on the rod by the pivot at this instant. solution Mg (c) Starting from the horizontal position, what initial angular speed would be needed...
A small 4-lb collar C can slide freely on a thin ring of weight
6 lb and radius 10 in. The ring is welded to a short vertical
shaft, which can rotate freely in a fixed bearing. Initially the
ring has an angular velocity of 35 rad/s and the collar is at the
top of the ring (θ = 0) when it is given a slight nudge. Neglecting
the effect of friction, determine a) the angular velocity of the
ring...
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