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
Importance of stresses in shaft: What is  importance of stresses in shaft ? Sol.: In shaft the following significant stresses occur. 1. A maximum shear stress occurs on

what is soundness of casting.

First Law for Closed System Undergoing Change of State - thermodynamics: In accordance to first law, when system undergoes a thermodynamic process (change of state) heat and w

Evaluate force and moment: What force and moment is transmitted to supporting wall at A   A force of 15 KN is transmitted to wall along with anticlockwise mome

Lifting machines: Basic definitions of the lifting machines and some lifting machines have been described. For each of these machines, derivation of the formulae for mechanica

PRE HEAT INTERPASS TEMP. REQUIREMENTS FOR FILLER METALS The preheat and inter pass temperature must be sufficient to prevent the  cracking.Previous  Experience has shown that t

Sentiment analysis is a subfield of NLP concerned with the determination of opinion and subjectivity in a text, which has application in the analysis of online product reviews, rec

Q. Materials used in insulation? All materials must be non-corrosive, compatible with other materials and used in accordance with the Manufacturer's recommendations. All mat

A mechanical System (two degrees of freedom system) is represented by the following two differential equations: m1x"1+(k1+k2)x1-k2x2=0 m2x"2-k1x1+(k2+k3) x2=0 Given m1=m2=0.5kg, k

Line of action of force: Sol.: The direction of force along the straight line through its point of application, in which force tends to move body to which it is applied. Thi