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
Consider laminar flow in a circular tubewith a fully developed velocity profile.Let the heat be added at a constant rate along the tube from  x+ =0  to  x+ =0.10 . Thereafter ,let

A square column 410 x 410 mm (along with 4 No. 16 mm bars) carries a dead load of 1020 kN and an imposed load of 410 kN. The foundation soil has a safe bearing capacity of 200 kPa.

There are five elastic properties needed to represent the elastic behaviour of a unidirectional laminate under in-plane loading, but only four of these are independent. The five

A lifting shackle in a glass-making factory is made from a special high-temperature stainless steel. It is expected that the shackle will experience a tensile load of 5kN and th

Find out the Moment of Inertia of a triangular area: Find out the Moment of Inertia of a triangular area ABC with base b and height d around its base BC. Therefore or otherwis


Follow board pattern This type of pattern is adopted for those castings where there are some portions which are structurally weak and if not supported properly are likely to br

Turnouts: A turnout is an assembly of various components whereby a train running on one track may be diverted to another. A sketch of a left-hand turnout is given in Figur

Evaluate the angle - block impends down the plane: What should be value of the angle shown in the figure so that the motion of the 90N block  impends down the plane? The coe

what are the parts of wilson hartnell governor with their designation?