Find out the maximum deflection in beam, Mechanical Engineering

Find out the maximum deflection in beam:

A beam of span 8m is loaded with UDL of 10 kN/m over the middle half portion. Discover the maximum deflection. EI is constant.

Solution

By symmetry,

RA  = RB

= (10 × 4 )/2

= 20 kN

2113_Find out the maximum deflection in beam.png

Figure

M = 20 x -(10 ( x - 2)2) /2-(10 ( x - 6)2)/2

= 20 x - 5 ( x - 2)2  - 5 ( x - 6)2                        ---------(1)

EI ( d 2 y/ dx2) = M= 20 x - 5 ( x - 2)2  - 5 ( x - 6)2         -------- (2)

EI dy/ dx = 20 x2 /2- 5 ( x - 2)3 /3-( 5/3) ( x - 6)3 + C1         . . . (3)

EIy = 10 x3 /3- (5/12)  ( x - 2)4  - (5/12)  ( x - 6)4  + C1  x + C 2          --------- (4)

at A,  x = 0,     y = 0,        C2  = 0

at B,    x = 8 m,      y = 0

0 =10 × 83/3 - (5 /12 ) (8 - 2)4  - (5/12 )  (8 - 6)4  + C1  × 8

C1 = - 145

EI (dy/ dx) = 10 x2/3  - (5/3) ( x - 2)3  - (5 /3)( x - 6)3  - 145

EIy = 10 x 3  /3 - (5 /12) ( x - 2)4  - (5/12)  ( x - 6)4  - 145 x

The maximum deflection at centre, since the beam is symmetrical and symmetrically loaded.

∴          EIymax  =((10 × 43 )/3) - (5/12)  (4 - 2)4  -  (5/12) ( 4 - 6)4  - 145 × 4

ymax= - 1120/3EI

Posted Date: 1/21/2013 5:45:21 AM | Location : United States







Related Discussions:- Find out the maximum deflection in beam, Assignment Help, Ask Question on Find out the maximum deflection in beam, Get Answer, Expert's Help, Find out the maximum deflection in beam Discussions

Write discussion on Find out the maximum deflection in beam
Your posts are moderated
Related Questions
Specific volume of the superheated steam: It is volume occupied by unit mass of superheated steam corresponding to given pressure of superheated steam generation. Superheated

Q. Mechanical Data for Line Designation Tables? Line Designation Tables (LDT's) are initially generated by the Piping designers. Design conditions are inputed by the Process di

(a) Derive a mathematical expression to determine the efficiency of Bell Coleman Cycle. (b) A dense air refrigeration cycle acts between pressures of 4 bar and 16 bar. The air t

Determine the ratio between moment and load: Any close coiled helical spring of circular section extends 1 mm while subjected to an axial load of W and then given an angular r

A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.0 m cables attached to a vertical rotating pole, as the drawing shows. (θ = 60.0°) Suppose the tota


Q. Process of polymerization? The process of linking together of monomers, that is, of obtaining macromolecules is called "polymerization". It can be achieved by one of the two

aframe of punching machine and its varios dimentions. if it has force of85kN determine others

To select the project, if not already done - Radial Drilling Machine Due to above Problem?s in RADIALL DRILLING machine, now the select the project and solves the problems and

How does an Ignition system works ?