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
Materials requirements planning: Materials requirements planning (MRP) is a set of process for converting forecasted demand for a manufactured product into a requirement sched

(a) What are the need of a surface condensing ? Write disadvantages and advantages of Jet condenser and surface condenser. (b) A surface condenser is designed to handle 10000 Kg

Q.   Describe the principle of energy conversion. Show that the reaction of coupling magnetic field on the electrical or mechanical system is essential for the electro - mechanical


The Continue Dimension Command You can use the Continue command to add a string of dimensions. In the illustration above the "36mm" dimension has been continued from the "64mm"


Classification Based on Type of Welding  Fusion welding : These processes involve fusion of the base metal to complete the weld. Fusion welds generally  do  not  require  thea

Calculate thermal efficiency and compression: Q: Calculate thermal efficiency and compression ratio for automobile working on otto cycle. If energy generated per cycle is t

Sales incentives , introduction of new models as well as variants coupled with easy availability of low cost finance with comfortable repayment options continues to drive demand an

Example of Process Capability The specifications for one characteristic of a part call for its width to be 3.000 + 0.008 centimetres. The procedure has been run under controll