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find the horizontal and vertical movement of each joint in the truss of problem 310 what are the forces in the
express the reissner functional for the cantilever beam shown in fig 436 having a triangular axial force distribution
for the continuous beam shown in fig 437 find the magnitude and direction of the centerline deflection of the right
determine the force of the spring for the beam shown in fig 438 using energy methods first consider the spring force as
find the deflection and slope at point a of the simply-supported beam shown in fig 439 using the second castigliano
it is desired to limit the centerline deflection of the spandrel beam fig 441 to 1288l where l is the length expressed
how large a moment is required at the free end of a cantilever beam to provide a slope there of thetax l 0036 inin
for the given frame find the horizontal deflection at a fig 445 would the deflection there vanish if q 0 explain all
a pipe see fig 446 in the vertical plane is fixed at a and b what are the supporting forces and moments at a and b if
find the bending moment along the portion ab of the rectangular frame shown in fig 449 one corner a is pinned the other
using same coordinate functions for the rectangular shaft as was used in sec 54 find the same approximate solution via
the cross section fig 514 is parabolic on top and bottom what are the equations of the upper and lower curves find an
estimate the torsional rigidity of a rectangular shaft 2a times 2b using as a coordinate function cos pix2a cos piy2b
find the total potential energy in terms of now find the quadratic functional for the equation 57a show that they
consider a clamped rectangular plate 0 le x le a 0 le y le b with a concentrated load at the center find an approximate
find an approximate ritz solution for the deflection at the center of a simplysupported square plate loaded by moment
consider a rectangular plate simply supported at the edges x 0 and y 0 while freely supported at the edges x a and y
find an approximate solution for the clamped circular orthotropic plate of radius a see problem 63 for a centrally
use the reissner principle to derive the mindlin-type improved plate theory for axisymmetric deformation of a circular
find the rayleigh quotient for torsional vibration of problem 78 what is the effect of the added masses on the free
using rayleighs quotient find the fundamental frequency of a stretched rectangular membrane supported at x 0 a and y
with the aid of eq a of problem 713 derive the rayleigh quotient for a circular membrane for axisymmetric deformation
in the preceding problem devise approximate eigenfunctions that satisfy the end conditions ofusing the rayleigh
derive the differential equations and boundary conditions for longitudinal vibrations of a uniform bar also obtain the
do the first part of problem 77 this time including the effects of two rigid cylinders respectively of uniform mass per