Flexural Design Procedure for Singly Reinforced Rectangular Beams

The following paragraphs summarize the design procedure for rectangular beams. Theprocedure can be easily extended to other shapes.

Design is an iterative process and there is no unique solution. The following is providedto give a general outline of the design process.

1. Design requirements (provided by code and/or others)a. Strength design - un MM ≥φb. Serviceability – small deflections and cracksc. Durability – corrosion and fire resistantd. Economical

2. Strength design requirementsa. Loading given.b. It is likely that the outline of structure has already been determined. Therefore,

span should be knownc. Find factored load using ASCE-7 load factors (Appendix C)

3. Select strength of reinforcing steel and concretea. Concrete strength of 3000 psi is commonly used for the design of beams protected

from weather and spanning moderate distances (25 to 30 ft.). 3000 psi concretehas sufficent strength and workability. Higher concrete strengths may be used toincrease durability (i.e., air entrained concrete) or for columns.

b. Steel strength normally 60 ksi. Higher strength steel may be used to reduce thearea of reinforcement required however the ducility of higher strength steels isreduced. Therefore, in seismic regions, it is common to use A 706 reinforcement.

4. Select beam dimensionsa. Find minimum thickness using ACI Table 9.5a

Minimum thickness, hFor members not supporting or attached to construction likely to be damaged by large

deflectionsMember Simply

SupportedOne end

continuousBoth ends

ContinuousCantilever

Solid one-wayslabs

l/20 l/24 l/28 l/10

Ribbed one-way slabs orBEAMS

l/16 l/18.5 l/21 l/8

b. Beam width, bTypically use d/b = 1.5 to 3.i) Shallow, wide beams:

easy bar placementmore headroomlower formwork costsless efficient

ii) Deep, narrow beams:minimum weight and steelmaximum stiffnessdifficult to place reinforcementlarge interstory heights.

c. Beam dimensions typically whole inches, multiples of 2 inches if possible; slabsand walls may be specified in ½-inch increments.

5. Analyze structure assuming elastic behavior, to find load effects. Typically, used aneffective moment of inertia for entire beam that is less than the uncracked moment ofinertia.

6. Select reinforcing ratioa. Find minimum steel area (ACI 10.5.1 and 10.5.2).

beams-T edeterminat staticallyfor /2006

/2003

'

min

'

min

ywwy

cx

ywwy

cx

fdbdbf

fA

fdbdbf

fA

>=

>=

b. Find maximum steel area. Use either ACI Chapter 9 (10.3.3) where

balρρ 75.0< or Appendix B for which tension failure corresponds to εs = 0.005.

Estimate depth of compression block for balanced failure using:

B)(Appendix 005.0for 375.0*

for 000,87

000,87

1

1

==

=

+

=

s

ysy

d

a

fd

a

εβ

εεβ

Therefore, these expressions can be used to find the balanced ratio.

d

a

f

f

y

cbal *

85.0 '

=ρ

c. Choose reinforcing ratio between the minimum and maximum steel limits.Reinforcing ratio should satisfy un MM ≥φ using either

i) design tables

[ ]'c

yc

u

f

fùf

bd

M ρωωφ =−= where59.01'

2

ii) this simple approximation which assumes fy = 60 ksi, φ = 0.8, and jd = 0.9d:

d

Ab

d

MA

s

us

ρ=

≥43

7. Select the bars to satify As. Determine the thickness of cover and spacing betweenbars according to ACI.

8

911

. Check actual beam strengthUsing the actual depth (d) and bars, determine the actual strength of the beam. Ensurethat un MM ≥φ . If this is satisfied, the beam design meets the minimum flexural

strength requirements. Otherwise, redesign beam dimensions and/or reinforcing ratioto meet the demand.

In additon, you must:

. Design shear reinforcement0. Check serviceability requirements1. Detail anchorage of reinforcement; check flexural bond requirements

We will do this in this later in the class.

• Place bars directly above bottom bars (ACI 7.6.2)• Use larger bars in bottom row, at least 2 bars per layer• Try to place bars in one row, no more than 6 bars per layer

Minimum clear spacingof 1 inch (ACI 7.6.1) or 1.33 times the diameter of coarseaggregate (ACI 3.3.2)

Minimum clear spacingof 1 inch or bar diameter (ACI 7.6.2)or 1.33 times the diameter of coarseaggregate (ACI 3.3.2)

• No more than two barssizes at any one location.• Bar sizes should notdiffer more than 2 sizes.• Use No. 11 bars orsmaller for normal-sizebeams.

Minimum cover for beams(ACI 7.7.1)Cast against earth - 3 in.Exposed to weather - 2 in.Not exposed to weather - 1.5 in.