Civil Engineering Reference
In-Depth Information
Example 20.1 illustrates the calculations necessary to determine the bending and
shear stresses and the maximum deflections that occur in the sheathing, joists, and
stringers used as the formwork for a certain concrete slab and live loading. In an actual
design problem, it may be necessary to consider several different arrangements of the
joists, stringers, and so on and the different grades of lumber available with their different
allowable stresses before a final design is selected.
EXAMPLE 20.1
3
4
-in.
The formwork for a 6-in.-thick reinforced concrete floor slab of normal weight consists of
Class II plyform sheathing supported by 2-
6-in. joists spaced 2 ft 0 in. on center, which in turn
are supported by 2-
8-in. stringers spaced 4 ft 0 in. on centers. The stringers are themselves sup-
ported by shores spaced 4 ft 0 in. on centers.
The joists and stringers are constructed with Douglas fir, coastal construction, and are to be
used many times. The allowable flexural stress in the fir members is 1875 psi, the allowable hori-
zontal shear stress is 180 psi, and the modulus of elasticity is 1,760,000 psi. For the plyform the cor-
responding values are 1330 psi, 72 psi, and 1,430,000 psi, with the stress applied parallel with the
face grain.
Using a live load of 150 psf, check the bending and shear stresses in the sheathing, joists, and
stringers. Check deflections assuming that the maximum permissible deflection of each of these ele-
ments is
/360 for all loads.
SOLUTION
Sheathing
Properties of 12-in.-wide piece of
3
4
plyform from Table 20.2:
Ib
Q
7.892 in.
2
S
0.455 in.
3
,
I
0.198 in.
4
,
Loads (neglecting weight of forms):
Concrete
(
12
)(150)
75 psf
LL
150
Total load
225 psf
Bending stresses (with reference made to Figure 20.5):
(225)(2)
2
10
2
10
w
M
90 ft- lb
f
b
(12)(90)
0.455
2374 psi
1330 psi
No good
Shear stresses (not usually checked in sheathing):
2
12
2
2
4
12
V
0.6
w
(0.6)(225)
253 lb
f
v
VQ
V
Ib
/
Q
253
7.892
32 psi
72 psi
Ib
OK
