Find out deflection under the load, Mechanical Engineering

Assignment Help:

Find out Deflection under the load:

A beam of span 4 m is subject to a point load of 20 kN at 1 m from the left support and a Udl of 10 kN/m over a length of 2 m from the right support.

Find out :

1. Slope at the ends.

2. Slope at the centre.

3. Deflection under the load.

4. Deflection at the centre.

5. Maximum deflection.

Take EI = 20 × 106 N-m2.

Solution

∑ Fy  = 0, so that RA + RB  = 20 + 10 × 2 = 40 kN         --------- (1)

275_Find out Deflection under the load.png

Figure

Taking moments around A,

RB  × 4 = 20 × 1 + 10 × 2 × 3 = 80

RB  = 20 kN                                                      -------- (2)

RA  = 20 kN

M = 20 x - 20 [ x - 1] - 10 [ x - 2] ([ x - 2]/2)

= 20 x - 20 [ x - 1] - 5 [ x - 2]2

EI (d 2 y/ dx2) = M

= 20 x - 20 [ x - 1] - 5 [ x - 2]2       ---------- (4)

 EI (dy / dx )= 10 x2 /3 - (10/3) [ x - 1]2  - (5/3) [ x - 2]3  + C1        ------ (5)

EIy = 10 x3 /3- (10/3) [ x - 1]3  - ( 5/12) [ x - 2]4  + C 1 x + C2  ---------6

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

at B, x = 4 m,      y = 0

0 =(10 × 43 )/3- 10 (4 - 1)3 - (5/12)  (4 - 2)4  + C 1 × 4

C1 =- 29.17

EI dy/ dx = 10 x2  - 10 [ x - 1]2  - (5 /3 )[ x - 2]3  - 29.17

 (a)       Slope at A, (x = 0),

θ A = - 29.17 / EI = - 29.17 × 10/(20 × 106)

 = - 1.46 × 10- 3  radians

(b)        Slope at B, (x = 4 m),

EI θB  = 10 × 42  - 10 (4 - 1)2  - 5 (4 - 2)3  - 29.17 = + 27.5

θB = + 1.38 × 10- 3  radians

 (c)       Slope at centre, (x = 2 m),

EI θC  = 10 × 22  - 10 (2 - 1)2  - 29.17

θC  = + 0.04 × 10- 3  radians

Deflection under the load :

EIy = 10 x3 /3- 10 [ x - 1]3  - (5/12)  [ x - 2]4  - 29.17 x

At x = 1 m,

EIy D = (10/3) - 29.17

EIyD  = - 25.84 × 103 × 103/20 × 106

= - 1.29 mm

 (d)      Deflection at the centre :

           x = 2 m

EIy =10 × 23 - (10/3) (2 - 1)3 - 29.17 × 2

yC  = - 1.75 mm

 (e)       Maximum deflection : Let the maximum deflection b/w D and C (x < 2 m).

dy/ dx = 0

10 x2  - 10 ( x - 1)2  - 29.17 = 0

10 x2  - 10 x2  - 10 + 20 x - 29.17 = 0

x = 1.96 m < 2 m

EIy max = (10/3) (1.96)3  - 10 (1.96)3  - 29.17 × 1.96 = - 35

∴ ymax  = - 1.7501 mm


Related Discussions:- Find out deflection under the load

Carnot cycle, what is mimnimum data for modelling a unique carnot cycle

what is mimnimum data for modelling a unique carnot cycle

Determine the carbon content of steel, Determine the carbon content of stee...

Determine the carbon content of steel: A hypoeutetoid steel which was cooled slowly from γ-state to room temperature was found to contain 10% eutectoid ferrite. Suppose no cha

Determine the pressure point for hydrostatic force, The 300 kg, 8-m-wide re...

The 300 kg, 8-m-wide rectangular gate shown in the figure is hinged at B and leans against the floor at A making an angle of 60° with the horizontal. The gate is to be open from it

What is the pressure difference between the stations , (Bernoulli equation ...

(Bernoulli equation along a streamline) Water flows from station (1) to (2) around an expanding corner pipe, 3m high. The speed along the center streamline is 10 m/s at (1) and 5

Solve the equations by factorization method, a) Answer the following equati...

a) Answer the following equations by Factorization method 10x+y+z =12 ; 2x+10y+z =13 ; 2x+2y+10z=14 b) Apply Gauss-Seidal Iteration method to solve the equations 20x+y-2z

Control, hey i really need someone to help doing my control course work asa...

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

Explain coating repairs, Q. Explain Coating Repairs? Any coatings found...

Q. Explain Coating Repairs? Any coatings found to be damaged or that do not pass the inspection stage shall be recoated or repaired at the expense of the Applicator. The entire

What is two way punching shear, What is Two Way Punching Shear? Two Way...

What is Two Way Punching Shear? Two Way Punching Shear In columns, generally the tendency of the column is to punch through the footing.  This also is to be considered in de

Can you use motor oil in a hydraulic system, Hydraulic fluid has to pass a ...

Hydraulic fluid has to pass a dissimilar set of standards than motor oil. Motor oil has tackifiers, lower sulfur content, and other ingredients that could solve harmful to the seal

__, what is magnetostriction?

what is magnetostriction?

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