squared property of parabola

Rotation - Rotating Vessel

When at rest, the surface of mass of liquid is horizontal at PQ as shown in the figure. When this mass of liquid is rotated about a vertical axis at constant angular velocity ω radian per second, it will assume the surface ABC which is parabolic. Every particle is subjected to centripetal force or centrifugal force CF = mω2x which produces centripetal acceleration towards the center of rotation. Other forces that acts are gravity force W = mg and normal force N.
 

008-rotating-vessel.gif

 

Problem 706 | Solution of Propped Beam with Decreasing Load

Example 03
The propped beam shown in Fig. P -706 is loaded by decreasing triangular load varying from wo from the simple end to zero at the fixed end. Find the support reactions and sketch the shear and moment diagrams
 

Propped with decreasing load from w at simple support to zero at the fixed end.

 

Problem 705 | Solution of Propped Beam with Increasing Load

Problem 705
Find the reaction at the simple support of the propped beam shown in Fig. P-705 and sketch the shear and moment diagrams.
 

Propped beam loaded with triangular or uniformly varying load

 

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