Determine the shape of the beam, Mechanical Engineering

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

Posted Date: 1/21/2013 7:41:59 AM | Location : United States







Related Discussions:- Determine the shape of the beam, Assignment Help, Ask Question on Determine the shape of the beam, Get Answer, Expert's Help, Determine the shape of the beam Discussions

Write discussion on Determine the shape of the beam
Your posts are moderated
Related Questions
how do I learn how to present velocity and acceleration diagram from a free space diagram

Q1. A short vertical column consists of a channel section with the dimensions shown in Figure 1(a). The column (part of a system used to support a machine) carries a compressive p

Q. Show the Welding Processes and Restrictions? Welding may be performed manually, semi-automatically and or automatically using any process or combination of processes accepte

Q. Explain working of Steam Sampling? Sample coolers shall be supplied by the Vendor. A common sample spillage trough shall also be provided by the Vendor, with a cover screen

can you give me a complete design of hydraulic fixture for turning and facing machine ? with all dimension an graph and analysis after apply the fixture

It is essential to select a flat belt drive for a compressor running at 720 r.p.m which is driven by a 25kW, 1440 r.p.m. motor. Space is available for a distance of 3m. The belt is

Introduction And Over View Of Various Manufacturing Process The main aim behind advances in engineering and technology has been to raise the standard of living of man and to ma


A semi circular frame of flexural rigidity EI is built at A and caries a vertical load W at B. calculate the magnitude of the vertical and horizontal deflection at B and hence the

Q. Steam Generator Master Pressure Control? The combined header pressure is controlled by a regular P.I.D. controller which ultimately trims the water flow to each boiler. A