by the way, jay, "what are the assumptions in calculating EI that may not be strictly true??"
i can't even find one
you know, by deflection, i plotted the mid-span moment(M) against the curvature(K). because M=EIk, the slope is the value of EI.
i think it is perfect..
units?
yeah, i am confused as well.
isnt N.mm^2? since E(N/mm^2) I(mm^4)
the experiment is to examining the stiffness of a steel beam through 2 types of deformation-deflection and curvature..
now i am writing the discussion part, but not many things to be mentioned.
Homework Statement
simply put, i got 2.1E+10 N.mm^5 for my steel beam experiment?
but i am wonder, what conclusions can i make?
2. The attempt at a solution
from online resouce, flexural rigidity is defined as the force couple required to bend a rigid structure to a unit curvature.
so ...
thanks Tim, in part a) of this question, i found the semi-axes of this elliptic paraboloid are b*sqrt((h-z)/h) and a*sqrt((h-z)/h)
therefore the intersection of the ellipse at height z is going to be [a*sqrt((h-z)/h)]*[b*sqrt((h-z)/h) ]*pi, isn't? which is just pi*(h-z)/h*a*b.
then how am i...
: ((
i am confused as well, but this is what is written in my textbook-'course notes for Math2061", University of Sydney, school of mathematics and statistics.
basically i think it is just using double integral to find the volume...
Tim, does that make sense?
OK.Tim, this is what i learn from my textbook.
If f(x,y)>=0 for all (x,y) in some region R, then z= f(x,y) represents a surface sitting above the xy-plane and over R. the double integral f(x,y) dxdy can then be interpreted as the colume of the solid under the surface z=f(x,y),over R, since the...
ok... i do this question like this.. tell me if i am right or not. : ))
let x = r∙cos(θ),y = r∙sin(θ)
dS = dxdy = r drdθ
because
x² + y² ≤ b² =>r²∙cos²(θ) + r²∙sin²(θ) ≤ b²=>r² ≤ b²
and r is the distance to the origin, which can not be negative. So the range of integration in radial direction...
Homework Statement
a elliptic paraboloid is x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h. Its apex occurs at the point (0,0,h). Suppose a>=b. Calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.:confused:
2. The attempt at a solution
We normally do the...
how can i set up x and y in polar coordinates??
we usually get a cylinder or whatever the intersection is a circle.
in these cases, x=rcos(),y=rsin()...
Tim, same equation for the solid elliptic paraboloid, x^2/a^2+y^2/b^2<=(h-z)/h, 0<=z<=h.
the question is : suppose a>=b, calculate the volume of that part of the paraboloid that lies above the disc x^2+y^2<=b^2.( use a suitable integral in polar coordinates.)