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
Seasonal-Component Analysis: A food processor uses a moving average to forecast next month's demand. Actual demand data for the past few months is available as depicted in the

The square cross sections A and B are shown in Fig Q1, the dimensions b = 80 mm, thickness t = 10 mm. A shear force V is applied at the cross section, calculate the maximum she

Determine the rate of heat removal: Carbon dioxide passing through heat exchanger at rate of 100kg/hr is cooled down from  800 0 C to 50 0 C . Write down the steady flo

HOW TO SIZE RECIRCULATION HOT WATER PUMP?

Are there jobs in the field of Mechanical Engineering that incorporate the outdoors? I am an outdoorsman for one, and a tradesman at heart and am currently a Mechanical engineering

Determine reactions at supports: Determine reactions at supports of supported beam of 6m span carrying increasing load of 1500N/m to 4500N/m from one end to another end.

how should we consider positive or negative when summation of forces

Discover the increase in pressure: A copper tube of 50 mm diameter and 1200 mm length contains a thickness of 1.2 mm along closed ends. This is filled with water at atmospheri

Q What do you know about Series welds in spot welding? It is a welding method in which two or more spots are produced simultaneously with only one common but indirect current p

Q. Show the Procedure of Compute flange stresses? Compute flange stresses and the actual bolt stress using: - COLT values for gasket seating stress, ‘y' and the gasket facto