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
Explain Function Phase of Hydrostatic sensor paver machine To identify the functions. To identify the functions regarding to the problem in paver machine. Our project focu

Lasers with Solid State Lasing Mediums For an active medium, the solid state laser uses lasing ions which are suspended in a rod shaped solid matrix. These "dopants" in the rod

Describe vortex flow and derive mathmetical equation Z= w 2 r 2 /2g for forced vertex flow ω= angular velocity z= height of parabola r= radius of parabola

Clutch-free Pedal Play : To reduce effective clamping load on the carbon thrust bearing and wear thereof, sufficient clutch free pedal play must be provided in the clutch.

A tensile test on a specimen having an initial diameter of 13.11 mm and an initial gauge length of 200.0 mm, gave the following data:

Derive and expression for force exerted by a jet of water on fixed vertical plate in direction of

hey i really need someone to help doing my control course work asap cuse it is due sunday it is about Control of water level in a nonlinear ‘V’ shaped tank

minimum mass of air required for complete combustion of the HFO


Find out the friction force: The cord passes over a massless and frictionless pulley, carrying a mass M 1 at one end and wrapped around a cylinder of mass M 2 which rolls on