Determine the shape of the beam, Mechanical Engineering

Assignment Help:

Determine the shape of the beam:

A simply supported beam of span l carries a concentrated load P at midspan. If the beam is to be a beam of consistent strength, determine the shape of the beam by keeping the width constant & varying the depth towards the supports.

Solution

Consider the beam has uniform width b during the span and let d be the maximum depth at midspan.

Consider dx be the depth of beam at any section XX, distance x from the support A.

Bending moment at section XX =  (P/2) x .

Moment of resistance of beam at section XX = (1/6) × σ × b × (d x)2

Moment of resistance = Bending moment at that section

 (1/6) × σ × b × (d x)2  = (P/2)x

720_Determine the shape of the beam.png

Therefore, the depth at any section at a distance x from the left support A might be found. The variation of the depth is illustrated in Figure .

 

Therefore, the depth at midspan, ( at x =  (½) ) , we get

 d =  ((3P/ σ b) ×  (l /2))(1/ 2)  =   ((3/2) ×  (Pl / σ  ))(1/2) .

1017_Determine the shape of the beam1.png

Simply Supported Beam


Related Discussions:- Determine the shape of the beam

Composites , For an automotive component of your choice that is traditional...

For an automotive component of your choice that is traditionally metallic, review how it could be re-engineered as a composite? How factors such as fibre & matrix type, fibre volum

What is the use of welding electrode, Q. What is the use of welding electro...

Q. What is the use of welding electrode? An electrode is a piece of wire or a rod (of a metal or alloy), with or without flux covering, which carries current for welding. Its o

Gear Transmission Systems, Develop a computer program for the “Gear Transmi...

Develop a computer program for the “Gear Transmission Systems” with consideration that each gear designer will have a different view as to what the most important design factors ar

Biofluids mechanics, in fontan circulation that is represented as a circuit...

in fontan circulation that is represented as a circuit

Entropy, Change in entropy for reversible

Change in entropy for reversible

TURBINE, Is it possible to rotate turbine blades without any fluid means th...

Is it possible to rotate turbine blades without any fluid means there is no requirement of water or air to rotate turbine blade. blades may rotates with the help of spring compress

Thermodaynamic, Ask question #MiThe steam that leaves the super-heater is e...

Ask question #MiThe steam that leaves the super-heater is expanded from 130bar at 535°C to 25.2bar at 310°C in a high pressure turbine. The steam from the exit of the HP turbine is

Explain the principle of screw conveyer, Explain the Principle of screw con...

Explain the Principle of screw conveyer When materials are feed into the fixed chutes, due to action of gravity of materials and the friction force between material and chute t

Buckingham''s pi-theorem, (a) Show by use of Buckingham's Pi-Theorem that t...

(a) Show by use of Buckingham's Pi-Theorem that the velocity through an orifice is given by V = √2gH  f D/H , M/ΡVH , σ/ΡV 2 H . Where H is the head causing flow, D is the diame

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