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
why does pressure and temperature rise after the process of compression


what do u you understand by steady state?


Process Selection in Making a Simple Part You should first determine the part's function, the types of load and environment to which it would be subjected, the dimensional to

Describe the basic concept of descriptive interface Descriptive interfaces are the window to other CAD systems, to the master databases or to the manufacturing activities. The

FRICTION: you have learnt laws of friction and problems involving dry friction. The relative sliding motion of one body on another body is resisted by forces called as frictio

Inventor claims in adiabatic system: On e inventor claims that 2 kg of air supplied to magic tube at 4 bar and 20°C and the two equal mass streams at 1 bar are produced, one

Traveling at a speed of 16.0 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the roa

Determine reactions at supports: Determine reactions at supports of supported beam of 6m span carrying increasing load of 1500N/m to 4500N/m from one end to another end.