Find out the maximum deflection in beam, Mechanical Engineering

Assignment Help:

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


Related Discussions:- Find out the maximum deflection in beam

What are the alluvial sediments, What are the Alluvial sediments Alluvi...

What are the Alluvial sediments Alluvial sediments are characterized by stratification or layering and fine grained soil layers have higher compressibility as compared to coars

Evaluate the angle - block impends down the plane, Evaluate the angle - blo...

Evaluate the angle - block impends down the plane: What should be value of the angle shown in the figure so that the motion of the 90N block  impends down the plane? The coe

Stroke and clearance volume - thermodynamics, Stroke and Clearance Volume: ...

Stroke and Clearance Volume: Stroke The distance traveled by piston from the topmost positions of it (also called Top dead centre TDC ), to its bottom most position (or

Prove the fourier series expansion, (a) Prove that the fourier series expan...

(a) Prove that the fourier series expansion for the function x(t) described in the finite interval -π ≤ t≤ π x(t) = 0 -π ≤ t ≤ 0 x(t) = sint 0 ≤ t ≤ π (b) Represent t

Calculate energy and entropy - thermodynamics, Thermodynamics. Justify that...

Thermodynamics. Justify that it is the science to calculate energy, energy and entropy. Sol : Thermodynamics is science which deals with conversion of heat into mechanical e

Determine the stability of the closed loop system, Determine the stability ...

Determine the stability of the closed loop system whose open loop transfer function is Use the Nyquist criterion

Determine the forces in all the members of the truss, A truss of span 10 me...

A truss of span 10 meters is loaded as shown in Figure. Determine the forces in all the members of the truss by Method of Joint.

Calculate change of entropy of universe, Calculate change of entropy of uni...

Calculate change of entropy of universe: 5Kg of ice at 10 0 C is kept in atmosphere that is at 30 0 C. Calculate change of entropy of universe when it melts and comes i

Introduction to welding processes, 1.0     INTRODUCTION Welding is a mat...

1.0     INTRODUCTION Welding is a material joining process used in making welds and a weld is a localised coalescence of metals or non metals produced either by heating the mate

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