# What is the Stress in Timber Beams?

Posted in Timber Engineering | Email This Post |Extreme fiber stress in bending for a rectangular timber beam is calculated by the following

f=6M/bh^{2}

=M/S

where

f= maximum fiber stress, lb/in^{2} (MPa)

M= bending moment, lb in (Nm)

h= depth of beam, in (mm)

b= width of beam, in (mm)

S= section modulus (bh2/6 for rectangular section), in^{3} (mm^{3})

The horizontal shearing stress in a rectangular timber beam is

H=3V/2bh

For a rectangular timber beam with a notch in the lower face at the end, the horizontal shearing stress is

H=(3V/2bd_{1})(h/d_{1})

where

h= depth of beam, in (mm)

b= width of beam, in (mm)

H= horizontal shearing stress, lb/in^{2} (MPa)

V= total shear, lb (N)

d_{1}= depth of beam above notch, in (mm)

l= span of beam, in (mm)

P= concentrated load, lb (N)

V_{1}= modified total end shear, lb (N)

W= total uniformly distributed load, lb (N)

x= distance from reaction to concentrated load in (mm)

**For simple beams**

Span should be taken as the distance from face to face of supports plus one-half the required length of bearing at each end

**For continuous beams**

Span should be taken as the distance between the centers of bearing on supports.

When determining V, neglect all loads within a distance from either support equal to the depth of the beam.

**For concentrated loads**

V^{1}=[10P(l-x)(x/h)^{2}]/9l[2+(x/h)^{2}]

**For uniform loading**

V^{1}=W[(1-2h/l)]/2

The sum of the V^{1} values from these equation should be substituted for V in the equation above and then the corresponding H value is calculated. This value is then checked with tables of allowable unit stresses for end-grain bearing.