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

Explain numerical control (n.c) procedure, Explain Numerical Control (N.C) ...

Explain Numerical Control (N.C) Procedure a) Process Planning: - This is listing of the sequence of operation to be performed during manufacturing of a part. This as well lists

Measurement of hardenability, Measurement of Hardenability: Two testi...

Measurement of Hardenability: Two testing techniques have been enhancement to measure the harden-ability of steels. The first, termed as cylinder series test, offers a single

Determine the maximum efficiency, A jet strikes tangentially a smooth curve...

A jet strikes tangentially a smooth curved vane moving in the similar direction as the jet, and the jet gets reversed in the direction. Prove that the maximum efficiency is slightl

Environments can cause deterioration of foundation, Environments can cause ...

Environments can cause deterioration of foundation. Can you explain this in the following cases? a) A column footing which was stable for a number of years suddenly gave way. T

What do you mean by an inertial reference, (a) Comment on the require to id...

(a) Comment on the require to idealise a body as a particles, a rigid body or a continuum. (b) What do you mean by an inertial reference ? (c) Define quantitatively a force 1

Calculate efficiency of turbine, (a) Explain briefly the functions of the s...

(a) Explain briefly the functions of the spiral casing guide vanes, and draft tube of a reaction water. (b) A Kaplan turbine developing 3250 KW under a head of 6m has a draft tu

Show prevailing wind conditions for plant layout, Q. Show Prevailing wind c...

Q. Show Prevailing wind conditions for plant layout? Prevailing wind conditions influence the design considerations for the location of the flare or vent stack. It is vital tha

Calculate the diameter of the single pipe, a) Three pipes of lengths 800m, ...

a) Three pipes of lengths 800m, 400m, 500m and of diameter 500mm, 400mm and 300mm respectively are connected in series. Pipes are to be removed by a single pipe of length 1700m. Ca

Define the winged-edge representation, The Winged-Edge Representation P...

The Winged-Edge Representation Perhaps the oldest data structure for a b-rep is Baumgart's winged-edge data structure. It is quite different from that of a wire-frame model, be

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