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

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Forms for Thin-Shell Roof Slabs 389
The maximum bending moment will occur at the center of the rib.
Summing the moments at the center of a rib,
M = (1,800 lb)(30 in.) – (1,200 lb)(24 in.)
= 25,200 in.-lb
An alternative method of calculating the maximum moment is by
using the equation for maximum moment of beam 5 in Table 5-2 as
follows:
M = P[l/4 + a]
= 1,200[60/4 + 6]
= 25,200 in.-lb
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Consider 2 × 10 No. 2 grade Southern Pine with a load duration
less than 7 days; Tables 4-2 and 4-4 give the allowable stresses:
Allowable bending stress, F b
= C D
× (reference bending stress)
= 1.25(1,050)
= 1,312 lb per sq in.
Allowable shear stress, F v
= C D
× (reference shear stress)
= 1.25(175)
= 218 lb per sq in.
The strength requirements for bending and shear will be considered,
but deflection criteria will not be considered. Following are
checks for bending and shear. For bending, the required section
modulus can be calculated as follows:
From Eq. (5-11), S = M/F b
= 25,200/1,312
= 19.2 in. 3
The rib should have a section modulus of at least 19.2 in. 3 An
inspection of Table 4-1 indicates that a 2 × 10 S4S section has a section
modulus of 21.39 in. 3 , which is greater than 19.2. Therefore the 2 × 10
is adequate for bending.
The rib must also have adequate shear strength. The maximum
shear force will occur at the support and is equal to 1,800 lb. The
shear stress in the rib can be calculated as follows:
From Eq. (5-13), f v
= 3V/2bd
= 3(1,800 lb)/2(1.5 in.)(9.25 in.)
= 194.6 lb per sq in.
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