Determine the width and depth of the beam, Mechanical Engineering

Determine the width and depth of the beam:

A timber beam of rectangular section is only supported over a span of 5 m. It carries an uniformly distributed load of 15 kN/m over the entire span. Determine the width and depth of the beam, if the bending stress is restricted to 8 N/mm2. The depth to width ratio might be taken as 1.5.

Solution

Span of beam, l = 5 m

Uniformly distributed load, w = 15 kN/m

Maximum bending moment at centre, M = wl 2/8

Thus,   M =15 × (5) 2/ 8

= 46.875 kN m

= 46.875 × 106 N mm

From the relationship, M / I = σ/ y , we get, I = (M × y )/ σ

i.e.

 (1/12) bd3   = ((46.875 ×106)/8 )×      (d /12)

bd2 = (46.875 × 10 6× 12) / 16

= 35.15625 × 106

Depth to width ratio, d/ b  = 1.5 or d = 1.5 b,

On substituting,   ∴ b (1.5b)2 = (35.15625 × 106 ) /2.25

b3 = 35.15625 × 10

= 15.625 × 106

Therefore, we get        b = 250 mm

d = 1.5 × 250 = 375 mm.

Thus, width of beam = 250 mm, and

Depth of beam = 375 mm

Posted Date: 1/22/2013 12:21:32 AM | Location : United States







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

Write discussion on Determine the width and depth of the beam
Your posts are moderated
Related Questions
Combined Rules           MOD (modified operation due date)                                 PN j = max (t + o j , t dj ) (SPT-Tr) (Truncated SPT)

LASER WELD OVERLAY I CLADDING This process brings the metal surface to a substantially higher temperature than in the heat treating process and results in a thin molten surface

Construct of a diagonal scale: During construct of a diagonal scale of RF = 1/48, displaying yards, inches and feet to represent a maximum length of 7 yards. Scratch a distanc


Illustrate about the three authors of IGES In 1977, the three authors of The Initial Graphics Exchange Specification were recognized collectively for their contributions to the

Define Cam - Application of Computers in Manufacturing CAM can be simply defied as "the application of computers in manufacturing." Most elaborately, CAM refers to the use


how is varignons theorem useful in engineering mechanics

Function of screw conveyor with auger "To spread the road making raw material on the road during the operation"An auger/cut off assembly for a floating screed asphalt paver. Th

Q. Show the Coating Application? Immediately following surface preparation, the cleaned pipe shall be uniformly preheated by a non-contaminating method to the application tempe