Find out the slope and deflection at the free end, Mechanical Engineering

Find out the slope and deflection at the free end:

Discover the slope and deflection at the free end of a cantilever shown in Figure. Take EI = 200 × 106 N-m2.

Solution

M =- 30 x - 60 [ x - 2] - 24 ( x - 3) (( x - 3)/ 2)

=- 30 x - 60 [ x - 2] - 12 [ x - 3]2           -------- (1)

EI d 2 y/ dx2 = M

=- 30 x - 60 [ x - 2] - 12 [ x - 3]2             ----------- (2)

EI (dy/ dx) = - 15 x - 30 [ x - 2] - 4 [ x - 3] + C1         --------- (3)

EIy =- 5 x - 10 [ x - 2] - [ x - 3] + C1 x + C2        ------------- (4)

1732_Find out the slope and deflection at the free end.png

 Figure

Boundary conditions are :

At B, x = 5 m, dy/ dx  = 0      ---------- (5)

At B, x = 5 m,  y = 0              --------(6)

From Eqs. (3) and (5)

0 = - 15 × 52- 30 (5 - 2)2 - 4 (5 - 3)3 + C1

∴          C1 = 677                               ---------- (7)

From Eqs. (4), (6) and (7)

0 =- 5 × 5 3- 10 (5 - 2)3 - (5 - 3) 4+ 677 × 5 + C2

∴          C2  =- 2474            -------- (8)

EI dy/ dx  = - 15 x2  - 30 [ x - 2]2  - 4 [ x - 3]3  + 677       --------- (9)

EIy = - 15 x3  - 10 [ x - 2]3  - [ x - 3]4  + 677 x - 2474 --------- (10)

At free end, i.e. at A, x = 0, From Eq. (9)

θ  = +   677 /EI =677 × 103/200´106 = 3385 × 10- 3  radians

From Eq. (10)

yA  =- 2474/ EI =- 2474 × 103 × 103/200 × 106 = - 12.37 mm

= - 12.37 mm ( ↓ )

Posted Date: 1/21/2013 5:53:03 AM | Location : United States







Related Discussions:- Find out the slope and deflection at the free end, Assignment Help, Ask Question on Find out the slope and deflection at the free end, Get Answer, Expert's Help, Find out the slope and deflection at the free end Discussions

Write discussion on Find out the slope and deflection at the free end
Your posts are moderated
Related Questions
Clutch cable routing : Ensure that the cable is routed as per standard routing, through the brackets provided.

1.0     INTRODUCTION Welding is a material joining process used in making welds and a weld is a localised coalescence of metals or non metals produced either by heating the mate

Brazing is a technique of joining two similar of dissimilar metal pieces together by heating the surfaces and by using a non-ferrous filler metal having its melting point above 42

Steam turbine comprises of stages, number and size of the stages depends upon the break horsepower of the turbine. The stage has set of moving and fixed blades. The moving blade

Q. What is Injection moulding? An important industrial method of producing articles of thermoplastics is injection moulding. The moulding material is loaded into a hopper from

Explain Cutting Speed - Cutting Parameters It is relative speed (V 1 ) between wheel and the Work piece. It is expressed in m/sec.   V=Cutting speed=V 1   =

Three Particle System Suppose we have two particles of masses  m 1  and  m 2   already fixed in space at distance  r 12  from each other. Let us bring in a third particle of

Q. can you explain Shell molds? These molds are prepared by pouring a mixture of sand and thermosetting resin over the heated surface of a metallic pattern, which results into

Q. Define Current for electrical resistance welding? - With other parameters kept constant, the temperature in resistance welding is regulated by controlling the magnitude a

temparature stresses in composite bars