Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 78

Table 3-13 Beam Dimensions for Neglecting Tension

Possible
selection bxh
(in. x in.)

h (required)
in. b (in.)

20 68.8

22 60.5

24 54.2

26 49.1

28 45.1 28 x 46

30 41.7 30 x 42

32 38.9 32 x 40

34 36.6 34 x 38

36 34.5 36 x 36

38 32.7 40 x 32

40 31.2

42 29.8

44 28.6

3.7.2 Beam Design Considering Torsion

It is important for designers to distinguish between two types of torsions: equilibrium torsion and compatibility
torsion. Equilibrium torsion occurs when the torsional resistance is required to maintain static equilibrium.
A simple beam supporting a cantilever along its span is an example of equilibrium torsion. For this case, if
sufficient torsional resistance is not provided, the structure will become unstable and collapse. External loads
have no alternative load path and must be resisted by torsion. Compatibility torsion develops where
redistribution of torsional moments to adjacent members can occur. The term compatibility refers to the
compatibility of deformation between adjacent parts of a structure. As an example, consider a spandrel beam
supporting an exterior slab. As load on the slab increases, so does the negative slab end moment, which induces
torsion in the spandrel beam. The negative slab end moment will be proportional to the torsional stiffness of
the spandrel beam. When the magnitude of the torsional moment exceeds the cracking torque, torsional cracks
spiral around the member, and the cracked torsional stiffness of the spandrel beam is significantly reduced.
As a result, some of the slab negative end moment is redistributed to the slab midspan.

For members in which redistribution of the forces is not possible (equilibrium torsion), the maximum factored
torsional moment, T u , at the critical section cannot be reduced (Section 11.5.2.1). In this case the design should
be based on T u .

For members in a statically indeterminate structure where redistribution of forces can occur (compatibility
torsion), the maximum factored torsional moment at the critical section can be reduced to T cr where

⎛

A cp
p cp

⎞

T cr =φ 4 λ ʹ f c ⎜ ⎟ . When T cr /4 < T u < T cr , the section should be designed to resist T u . It is important to

⎝ ⎠

note that the redistribution of internal forces must be considered in the design of the adjoining members.