Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

104 Chapter Five
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From Eq. (5-18), the modified shear force for a multiple-span
beam with a uniformly distributed load can be calculated as follows:
V = 5wL/8[1 – 2d/l]
= [5(500 lb/ft × 2.5 ft)/8][1 – 2(3.5 in.)/30 in.)]
= (781.2 lb)[1 – 0.233]
= 598.9 lb
From Eq. (5-19), the applied shear stress can be calculated:
f v
= 15w[l – 2d]/192bd
ww.EasyEngineering.n
= 15(500 lb/ft)[(30 in. – 2(3.5 in.)]/[192(1.5 in.)(3.5 in.)]
= 172,500/1,008
= 171.1 lb per sq in.
Table 4-3 shows an allowable shear stress F v
as 150 lb per sq in.,
which is less than the calculated applied shear stress of 171.1 lb per sq
in. Therefore, the beam is not satisfactory for shear stress.
Example 5-3 showed the 2 × 4 beam adequate for bending using
the No. 2 grade Hem-Fir, but this example shows it is not adequate
for shear. A different grade and species of lumber could be considered.
For example, a No. 2 grade Southern Pine has an allowable
shear stress of 175 lb per sq in., or a No. 2 grade Douglas Fir-Larch,
which has an allowable shear stress of 180 lb per sq in. Either of these
grades and species would be adequate for shear. The beam should
also be checked for deflection as shown in the following sections.
Deflection of Beams
When a beam is subjected to a load, there is a change in its shape. This
change is called deformation. Regardless of the magnitude of the
load, some deformation always occurs. When a force causes bending
moments in a beam, the deformation is called deflection. A beam may
have adequate strength to resist applied bending and shear stresses,
but it may not have adequate rigidity to resist deflections that are created
by the loads applied on the beam. Some amount of deflection
exists in all beams, and the designer must ensure that the deflection
does not exceed the prescribed limits.
The amount of permitted deflection is generally specified in the
design criteria. Local building codes should also be consulted for specific
provisions governing deflection. Typically, the deflection is limited
to l/360 when appearance or rigidity is important. Limiting deflection
to l/360 reduces the unattractive sag of beams and reduces the
effect of an excessively springy floor. When appearance or rigidity is
less important, the deflection is sometimes limited to l/270 or l/240.
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