Points of contraflexure, Mechanical Engineering

Assignment Help:

Points of Contraflexure:

Assume M1, M2, . . . and M6 be the points of contraflexure, where bending moment changes sign. To determine the position of M2, let a section XX at a distance x from the end C.

M x  = - 15.2 x + 24

- 15.2x + 24 = 0

∴          x2  = 1.579 m

To determine the position of M3 and M4, consider a section XX at a distance x from the end E.

M x   = 15.2x + 24 + 30 ( x - 3) - (( ½) ( x - 3) × 0.6 × ( x - 3) × (( x - 3)/3)

M x  = - 15.2 x + 24 + 30 x - 90 - 0.1 ( x - 3)3

= 14.8 x - 66 - 0.1 ( x - 3)3

= 14.8 x - 66 - 0.1 [ x3  - (3 × π2 × 3) + (3x × 9) - 33 ]

= 14.8x - 66 - 0.1 ( x3  - 9 x2  + 27 x - 27)

=- 0.1x3  + 0.9 x2  + 12.1x - 63.3

On changing the sign and equating it to zero, we obtain

0.1x3  - 0.9 x2  - 12.1 x + 63.3 = 0

Solving out by trial and error, we obatin

x1  = 4.4814 m

x2  = 14.357 m

 and    x3  = - 9.84 m

As, the value of x3 is negative, it must be ignored.

To determine the position of M3, assume a section XX at a distance x from the end E.

M x=  7.2 × x × (x /2) + 15.6

On equating it to zero, we obtain

- 3.6 x2 + 15.6 = 0

x = 2.082 m

The points of contraflexure are at distance of 1 m, 1.579 m, 4.4814 m & 14.357 m from the left end X & at distances of 1 m & 2.082 m from the right end F.


Related Discussions:- Points of contraflexure

Thermodynamics, What are significnces of quasi static process

What are significnces of quasi static process

Kinematics in one and two dimensions , A person climbs up a escalator in 60...

A person climbs up a escalator in 60s . When he stands on it , then he is carried in the moving escalator in 30s . How much time will he take in climbing up in a moving escalator?

Turbine, What is the definition of stall

What is the definition of stall

Evaluate an expression for minimum number of teeth, Evaluate an expression ...

Evaluate an expression for minimum number of teeth on the wheel if interference is to be avoided between two mating gears. Also determine the above expression if gear ratio is equa

Sand blasting handling method, Sand blasting handling method:        ...

Sand blasting handling method:             On last experiment we had decided to use 3.0 bars as it shown better result. Now we had to investigate the sand blasting handling

Example of reduce system to a single force and couple, Example of Reduce sy...

Example of Reduce system to a single force and couple: A system of parallel forces is acting on rigid bar as shown in the figure given below. Reduce this system to  a sing

Estimate the horizontal at equilibrium angel, (Rigid body acceleration) A ...

(Rigid body acceleration) A tank of water accelerates down an icy frictionless ramp of angle . What angle ( ) does the water make with the horizontal at equilibrium?

Piping material specifications, Q. Show Piping Material Specifications? ...

Q. Show Piping Material Specifications? Piping Material Specifications include the development and / or review of material specifications, and the review of data sheets, materi

Determine the interface temperature, A steel pipe with 50 mm OD is covered ...

A steel pipe with 50 mm OD is covered with a 6.4 mm asbestos insulation followed by a 25 mm layer of fiber-glass insulation [K = 0.0485 Wmk]. The pipe temperature is 393 K and the

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