Determine the slopes at free end - cantilever beam, Mechanical Engineering

Determine the slopes at free end - cantilever beam:

A cantilever beam of length l carries a point load W at a distance l  /4 from free end.

Determine the slopes at free end and under load and the maximum deflection and deflection under the load.

Solution

M =- w [x - l/4 ]------------- (1)

EI (d 2 y /dx2)   =- w [x - l /4]                ------------ (2)

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

 EI y     =- (w/6)[x- (l/4)]3+  + C1  + C2                ------- (4)

1518_Determine the slopes at free end.png

Figure

Boundary conditions are :

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

At B, x = l, y = 0                         --------- (6)

From Eqs. (3) and (5),

0 =-     w/2 [l -l/4]2           + C1

C1  =+ 9 wl 2 / 32                          ------------. (7)

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

0 =- (w/6)[l-(l/4 ) 3+ 9 wl 3/32+C2

C2  = (wl 3 / (6 × 64)) [- 108 + 27]

=-81wl 3/ (6 × 64)        = - 27 w l 3/128        ---------- (8)

The Eqs. (3) and (4) will be :

∴          EI (dy/ dx)  =- (w/2) [x-(l/4)]2 + 9 wl 2/32             ------------ (9)

EIy = (w/6)[l-(l/4 ) 3+ 9 wl 3/32-27 wl3/128           ---------- (10)

Slope at A, (x = 0),

θA = +  9 wl 2 / 32EI          ---------------(11)

Slope at C, (x = l/4) ?,

 Θc = + 27 wl 2 / 128EL         

Deflection at A, (x = 0),

y A  =-27 wl3/ 128 EI       -------------- (12)

Deflection under load at C, (x = l/2) ,

=(9 wl 2 /32 ).(l/4) -27 wl 3  /128  =  - 18 wl 3/128------------ (13)

∴ yC  =- 18 wl 3 / 128 EI

Posted Date: 1/21/2013 5:50:36 AM | Location : United States







Related Discussions:- Determine the slopes at free end - cantilever beam, Assignment Help, Ask Question on Determine the slopes at free end - cantilever beam, Get Answer, Expert's Help, Determine the slopes at free end - cantilever beam Discussions

Write discussion on Determine the slopes at free end - cantilever beam
Your posts are moderated
Related Questions
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane, then wha

STEA M ENGINE TERMINOLOGY: 1 .     Cylinder Bore: Inside diameter of cylinder. 2 .     Cover End and Crank End of cylinder: In the horizontal cylinders the end that

Working of lacashire boiler: WORKIN G: Water is filled through feed check valve. On burning fuel over grate, the hot gasses are produced which move in flue gas tubes.

A space craft ‘A' has velocity 0.9 c relative to the earth. Another spacecraft ‘B' overtakes A with relative velocity 0.5 c. Find the velocity of spacecraft B relative to the groun

(a) Split up the harmonic x = 8 sin(ωt + 45°), into two harmonic motions, one of which has amplitude of 10 and phase difference zero. (a) A body is subjected to two harmonic mot

Write a MATLAB program to find the undamped natural frequencies and modes of an electric car treating it as a four degree of freedom system. Determine the undamped natural frequenc

Application of group technology point wise

Rutile Electrode This type has thicker coating than cellulosic coated and the flux is mainly composed of rutile (titanium di - oxide) and silicates, with a negligible amount of c

Q. Explain about Horizontal Vessels? Horizontal vessels shall preferably be designed for two saddle supports attached by welding. Design of saddle supports and calculation of