Reference no: EM13319602
column bending under its own weight: A uniform thin column of length L, positioned vertically with one end embedded in the ground, will deflect, or bend away,from the vertical under the influence of its own weight when its length or height exceeds a certain critical value.It can be shown that the angular of the deflection θ(x) of the column from the vertical at a point p(x) is a solution of the boundary-value problem:
EI (d^2 θ)/(dx)^2 + δg(L-x)θ=0 , θ(0)=0 , θ^' (L)=0,
where E is young's modulus, I is the cross-sectional momment of inertia,δ is the constant linear density, and x is the distance along the column measured from its base.
(a) restate the boundary-value problem by making the change of variable t=L-x. Then use the result of the problem earlier in this exercise set to express the general solution of the differential equation in terms of bessel funtion.
(b) use the general solution found in part (a) to find a solution of the BVP and an equation which defines the critical length L, that is, the smallest value of L for which the column will start to bend.
(c) with the aid of a CAS, find the critical length L of a solid steel rod of radius r=0.05in, δg=0.28 A Ib/in,E=2.6 x 10^7 Ib/in^2, A = πr^2, and I= (1/4)πr^4.
|
Calculate its rotational kinetic energy
: A metal rod (2.4 kg, 1.5 m long) is rotating about an axis through its center at 20.0 rad/s. Calculate its rotational kinetic energy
|
|
What will be allowable compressive stress in extreme fibers
: A) Compute the maximum fiber stress. B) If the compression flange of the beam is supported laterally only at the ends of the span, what will be the allowable compressive stress in the extreme fibers
|
|
Explain what is emperical formula
: Florine is so reactive that it forms compound with material insert to other treatment when 0.448gm of plantinum is heated in florine, 0.71gm of dark red, volatile solid forms. What is emperical formula
|
|
U.s. treasury bond issues. discuss the short-term and long
: Since the early 1980s, foreign portfolio investors have purchased a significant portion of U.S. treasury bond issues. Discuss the short-term and long-term effects of foreigners’ portfolio investment on the U.S. balance of payments.
|
|
Find solution of bvp and equation which defines critical l
: A uniform thin column of length L, positioned vertically with one end embedded in the ground, will deflect, or bend away,from the vertical under the influence of its own weight
|
|
Explain the reaction goes to completion
: Fe2O3 + 3CO------2Fe + 3Co2 suppose that 1.14x 10^3kg of Fe is obtained from 1.82x 10^3 kg of samples Fe2O3. Assuming that the reaction goes to completion. What is % purity of Fe2O3 in orginal sample
|
|
Capital from foreign countries to finance its current
: Comment on the following statement: “Since the U.S. imports more than it exports, it is necessary for the U.S. to import capital from foreign countries to finance its current account deficits.”
|
|
Is it desirable to have continuous current account surpluses
: In contrast to the U.S., Japan has realized continuous current account surpluses. What could be the main causes for these surpluses? Is it desirable to have continuous current account surpluses?
|
|
Estimate the magnitude of the normal force
: An 1840 kg car is driving at a constant speed of 12m across a bridge shaped in an arc with a rdius of 22m. Calculate the magnitude of the normal force the bridge exerts on the car
|