Simplified Design for Beams and One-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 51

0.5 × 0.0103 × 60, 000

⎡
⎢

⎤
⎥

= 0.0103 × 60, 000 1 −

0.85 × 4000

= 562psi

M u M u × 12 × 1000

bd reqd =

R n =

= 23.7M u

φ 0.9 × 562

For simplicity, set bd 2 reqd = 20M u which corresponds to ρ = 0.0125

For › = 4000 psi and f y = 60,000 psi:
bd 2 = 20M u
where M u is in ft-kips and b and d are in inches

A similar sizing equation can be derived for other material strengths. Figure 3-3 shows values for section sizing
for different concrete strengths and reinforcement ratios.

With factored moments M u and effective depth d known, the required beam width b is easily determined using
the sizing equation bd 2 = 20M u (for › = 4000 psi and f y = 60,000 psi). When frame moments vary, b is
usually determined for the member which has the largest M u ; for economy, this width may be used for all
similar members in the frame. Since slabs are designed by using a 1-ft strip (b = 12 in.), the sizing equation
can be used to check the initial depth selected for slabs; it simplifies to d = 1.3

M u

.

If the depth determined for control of deflections is shallower than desired, a larger depth may be selected with
a corresponding width b determined from the above sizing equation. Actually, any combination of b and d could
be determined from the sizing equation with the only restriction being that the final depth selected must be
greater than that required for deflection control (Table 3-1).

It is important to note that for minimum beam size with maximum reinforcement, the sizing equation becomes
bd 2 min = 14.6M u .

3.3.1 Notes on Member Sizing for Economy

￿ Use whole inches for overall beam dimensions; slabs may be specified in 1 / 2 -in. increments.
￿ Use beam widths in multiples of 2 or 3 inches, such as 10, 12, 14, 16, 18, etc.

￿ Use constant beam size from span to span and vary reinforcement as required.

￿ Use wide flat beams (same depth as joist system) rather than narrow deep beams.

￿ Use beam width equal to or greater than the column width.

￿ Use uniform width and depth of beams throughout the building.

See also Chapter 9 for design considerations for economical formwork.