Evaluate the deflection at the free end of the cantilever, Mechanical Engineering

Evaluate the deflection at the free end of the cantilever:

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

Solution

Apply Udl in both the upward and downward directions in the portion CB.

1275_Evaluate the deflection at the free end of the cantilever.png

 Figure

477_Evaluate the deflection at the free end of the cantilever1.png

 Figure

M = - 24 x . (x/2) + 24 ( x - 1) (( x - 1)/2) - 30 [ x - 2]

= - 12 x2  + 12 [ x - 1]2  - 30 [ x - 2] --------- (1)

EI (d 2 y /dx2 )= M = - 12 x 2  + 12 [ x - 1]2 - 30 [ x - 2]        ----------- (2)

EI dy/ dx = - 4 x3 + 4 [ x - 1]3 - 15 [ x - 2] 2+ C1        --------- (3)

EIy =- x + [ x - 1] - 5 [ x - 2] + C1 x + C2            --------------- (4)

The boundary conditions are :

 At B, x = 4 m, dy/ dx  = 0         -------- (5)

At B, x = 4 m,  y = 0                       ----------- (6)

From Eqs. (3) and (5)

0 = - 4 × 4 3+ 4 (4 - 1) 3- 15 (4 - 2)3 + C1

∴          C1 = 208                   ----------- (7)

 From Eqs. (4), (6) and (7)

0 =- 4 4+ (4 - 1)4 - 5 (4 - 2) 3+ 208 × 4 + C2

∴          C2  = - 617                  --------- (8)

∴          EI (dy / dx )=- 4 x3  + 4 [ x - 1]3  - 15 [ x - 2]2  + 208         ---------- (9)

EIy =- x4  + [ x - 1]4  - 5 [ x - 2]3  + 208 x - 617-------- (10)

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

 θ A = + 208 /EI = + 208 × 10/200 × 106 = + 1.04 × 10- 3  radians

From Eq. (10)

yA  =     617/EI = - 617 × 103 × 103 / 200 × 106 = - 3.085 mm ( ↓ )

Posted Date: 1/21/2013 5:55:56 AM | Location : United States







Related Discussions:- Evaluate the deflection at the free end of the cantilever, Assignment Help, Ask Question on Evaluate the deflection at the free end of the cantilever, Get Answer, Expert's Help, Evaluate the deflection at the free end of the cantilever Discussions

Write discussion on Evaluate the deflection at the free end of the cantilever
Your posts are moderated
Related Questions
Estimate the Weight of the Casting A Yoke casting shown in Figure is to be produced by sand casting process. Estimate the weight of the casting if the density of the material

How is angle of dispersion used in footing? Angle of Dispersion Indian Standards (IS) has specified relation for determining the angle, of dispersion. According to IS the an

A steam boiler, 3 m in diameter, is made of 25 mm thick mild steel plates. The efficiency of longitudinal riveted joint is 88% and that of circumferential riveted joint is 70%. Cal


Q. Use of high temperature material Flare Tips? A variety of high temperature alloys (typically stainless steels and/or nickel-base alloys) are employed in the construction of

Find out the smallest force: A block weighing 800 N is raised up with the help of two 6o wedges B and C of negligible weights as illustrated in Figure. If the coefficient of s

In Tools and equipment we studied about the various tools and equipment used in service and repair of a motorcycle and for the troubleshooting. Acquainting with these will help you

Principle of equilibrium: Sol.: Principle of equilibrium can be divided in to three main parts; (1) Two Force Principle: As the Resultant is zero when body is in equili


How can I achieve a back and forth movement of carriage system. How can I reverse the motor to go back and forth.