in design is given by v = \Q(a/d)
2
vY{9[2 + (a/d)
2
]}, where v = true maximum shearing
stress, IMn
2
(kPa); v' = nominal maximum stress computed from 1.5V/A; a = distance
from load to adjacent support, in (mm).
Computing the reaction R at the adjacent support gives R = Fmax = 2730(12 - 2)712 =
2275 Ib (10,119.2 N). Then v' = 1.5V/A - 1.5(2275)724.9 = 137 lb/in^2 (944.6 kPa).
- Find the design stress
Using the equation given in step 1, we get (aid)^2 = (24/9.5)^2 = 6.38; v = 10(6.38)( 137)/
[9(8.38)] = 116 lb/in^2 (799.8 kPa) < 120 lb/in^2 (827.4 kPa). The load is therefore not ex-
cessive.
SHEARING STRESS CAUSED BYMOVING
CONCENTRATED LOAD
A4 x 12 in (101.6 x 304.8 mm) beam on a span of 10 ft (3.0 m) carries a total uniform
load of 150 Ib/lin ft (2189.1 N/m) and a moving concentrated load. If the allowable shear-
ing stress is 130 lb/in^2 (896.4 kPa), what is the allowable value of the moving load as gov-
erned by shear?
Calculation Procedure:
- Calculate the reaction at the support
The transient load induces the absolute maximum shearing stress when it lies at a certain
critical distance from the support rather than directly above it. This condition results from
the fact that as the load recedes from the support, the reaction decreases but the shear-
redistribution effect becomes less pronounced. The approximate method of analysis rec-
ommended in the Wood Handbook affords an expedient means of finding the moving-
load capacity.
Place the moving load P at a distance of 3d or^1 AL from the support, whichever is less.
Calculate the reaction at the support, disregarding the load within a distance of d there-
from.
Thus, 3 d = 2.9 ft (0.884 m) and^1 AL = 2.5 ft (0.762 m); then R = Fmax = 150(5 - 0.96)
+^3 AP = 610 + V 4 P. - Calculate the allowable shear
Thus, Fallow =^2 AvA =^2 / 3 (130)(41.7) = 3610 Ib (16,057.3 N). Then 610 +^3 AP = 3610; P =
4000 Ib (17,792.0 N).
STRENGTH OF DEEP WOODEN BEAMS
If the allowable bending stress in a shallow beam is 1500 lb/in^2 (10,342.5 kPa), what is
the allowable bending moment in a 12 x 20 in (304.8 x 508.0 mm) beam?
Calculation Procedure:
- Calculate the depth factor F
An increase in depth of a rectangular beam is accompanied by a decrease in the modulus