CIVIL ENGINEERING FORMULAS

160 CHAPTER SIX

V 1 modified total end shear, lb (N)

Wtotal uniformly distributed load, lb (N)

xdistance from reaction to concentrated load in (mm)

For simple beams, the span should be taken as the distance from face to face of
supports plus one-half the required length of bearing at each end; and for continu-
ous beams, the 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.
In the stress grade of solid-sawn beams, allowances for checks, end splits, and
shakes have been made in the assignedunit stresses. For such members, Eq. (6.2)
does not indicate the actual shear resistance because of the redistribution of shear
stress that occurs in checked beams. For a solid-sawn beam that does not qualify
using Eq. (6.2) and the Hvaluesgiven in published data for allowable unit stresses,
the modifiedreactionV^1 should be determined as shown next.
For concentrated loads,

(6.4)

For uniform loading,

(6.5)

The sum of the V^1 values from Eqs. (6.4) and (6.5) should be substituted for V
in Eq. (6.2), and the resulting Hvalues should be checked against those given
in tables of allowable unit stresses for end-grain bearing. Such values should be
adjusted for duration of loading.

COLUMNS

The allowable unit stress on timber columns consisting of a single piece of
lumber or a group of pieces glued together to form a single member is

(6.6)

For columns of square or rectangular cross section, this formula becomes

(6.7)

P

A



0.30E

(l/d)^2

P

A



3.619E

(l/r)^2

V^1 

W

2 

1 

2 h

l

V^1 

10 P(lx) (x/h)^2

9 l[2(x/h)^2 ]