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

Assignment Help:

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


Related Discussions:- Determine the slopes at free end - cantilever beam

Explain ash handling system, Illustrate the following : a. Ash handling ...

Illustrate the following : a. Ash handling system b. Dust collection What are the impurities in the water and how they are replaced for use as feed water in modern thermal

Objectives of motorcycle servicing , Objectives After studyingmotercyc...

Objectives After studyingmotercycle servicing, you should be able to appreciate the importance of regular servicing and maintenance of a motorcycle and also to recommen

Thermal, mean effective pressure of dual cycle

mean effective pressure of dual cycle

Welding procedure and performance qualification, WELDING PROCEDURE AND PERF...

WELDING PROCEDURE AND PERFORMANCE QUALIFICATION A total quality assurance scheme, embracing all aspects of manufacture would have necessarily made all attempts to ensure

Free body diagram - mechanics, Free body diagram: Sol.: In a free bod...

Free body diagram: Sol.: In a free body diagram, the body is considered by itself and also the effect of the surroundings on the body is shown by forces and moments. Free bod

Modulus of elasticity, Explain Young's Modulus or Modulus of elasticity? ...

Explain Young's Modulus or Modulus of elasticity? Sol. : It is ratio between tensile stress and tensile strain or compressive stress and compressive strain. It can be denote

Objectives of general safety and service tips , Objectives After study...

Objectives After studying this general safety and services tips, you should be able to appreciate the importance of safety precautions, accomplish the servicing wo

Find the weight percent of austenite present in the steel, Find the weight ...

Find the weight percent of austenite present in the steel: A 0.4% C hypoeutectoid plain carbon steel is slowly cooled from 1540 o C to (i) slightly above 723 o C and (ii) s

Example of process capability, Example of Process Capability The speci...

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

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd