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

Ask an Expert

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

Write your message here..

Related Questions

Som, a steel bar is a steel bar is

Thermal stress, how did the formula derived smax = Ed1 a ?T/d 2 how did the formula derived smax = Ed1 a ?T/d 2

Manufacturing process, what is clapper box what is clapper box

Describe loose piece pattern, Loose piece pattern This type of pattern ... Loose piece pattern This type of pattern is also used when the contour of the part is such that withdrawing the pattern from the mould is not possible. Hence during moulding th

Alternating current -fundamentals of electricity , Alternating Current ( A... Alternating Current ( AC ) : The electricity whose direction changes at regular interval is known as alternating current. I

Wave motion, Wave motion takes place all throughout nature, from the waves... Wave motion takes place all throughout nature, from the waves of the ocean to the electromagnetic waves that comprise visible light. Though different types of waves involve differe

What do you mean by weld and hold time, Q. What do you mean by Weld and hol... Q. What do you mean by Weld and hold time? Weld time During this period the welding current flows through the circuit, i.e., it enters from one electrode, passes through t

Stenght of Material, Give the assumption of pure torsion derivation of shea... Give the assumption of pure torsion derivation of shear stress produced in circular shaft subjected to torsion

Arc strikes-metallurgical defects, Arc strikes Represent any localised ... Arc strikes Represent any localised heat affected zone caused by an arc. Arc strike tends to produce hardening particularly in high carbon steels and alloy steels. Grinding of

Velocity ratio for open belt drive, V elocit y Ratio for Open Belt Drive:... V elocit y Ratio for Open Belt Drive: Figure Consider a simple belt drive (that is one driver and one follower) as shown in the figure given below Let D 1