181

B- Columns of Special Moment Frames

ACI 18.7 applies to columns of special moment frames that form part of the

seismic- force-resisting system and proportioned primarily to resist flexure, shear

and axial forces. This section applies to columns of special moment frames

regardless of the magnitude of axial force. Before 2014, the Code permitted

columns with low levels of axial stress to be detailed as beams

1- Dimensional Limits:

ACI 18.7.2 requires that the following conditions are to be satisfied:

The shortest cross-sectional dimension, measured on a straight line passing

through the geometric centroid, shall not be less than 30 cm.

The ratio of shortest cross-sectional dimension to the perpendicular

dimension shall not be less than 0.40.

2- Minimum Flexural Strength of Columns:

Based on ACI 18.7.3.2, The flexural strengths of the columns shall satisfy

the following equation:

nbnc

MM 2.1

where

ncM = sum of nominal flexural strengths of columns framing into the joint,

evaluated at the faces of the joint. Column flexural strength shall be calculated

for the factored axial force, consistent with the direction of the lateral forces

considered, resulting in the lowest flexural strength.

nbM = sum of nominal flexural strengths of the beams framing into the joint,

evaluated at the faces of the joint. Flexural strengths shall be summed such that

the column moments oppose the beam moments.

The intent of the above equation is to reduce the likelihood of inelastic action.

If columns are not stronger than beams framing into a joint, flexural yielding

can occur at both ends of all columns in a given story, resulting in a column

failure mechanism that can lead to collapse.

For columns not satisfying the previous equation, the lateral strength and

stiffness of these columns shall be ignored when calculating strength and

stiffness of the structure. These columns shall conform to ACI 18.14

(frame members not proportioned to resist forces induced by earthquake

motions).

182

Strong column-weak beam requirements for special moment frames

3- Longitudinal Reinforcement:

ACI 18.7.4 requires that the following conditions are to be satisfied:

Area of longitudinal reinforcement, stA shall be at least gA01.0 and shall

not exceed gA06.0 . The lower limit of the area of longitudinal

reinforcement is to control time-dependent deformations and to have the

yield moment exceed the cracking moment. The upper limit of the area

reflects concern for reinforcement congestion.

In columns with circular hoops, there shall be at least six longitudinal

bars.

Lap splices are permitted only within the center half of the member

length, and shall be designed as tension lap splices and enclosed within

transverse reinforcement conforming to ACI 18.7.5.2 and 18.7.5.3.

183

Typical lap splice details of columns in special moment frames

4- Transverse Reinforcement:

Transverse reinforcement required in ACI 18.7.5.2 through 18.7.5.4 shall be

provided over a length l from each joint face and on both sides of any

section where flexural yielding is likely to occur as a result of lateral

displacements beyond the elastic range of behavior. The length l shall be at

least the largest of (a) through (c):

(a) The depth of the column at the joint face or at the section where flexural

yielding is likely to occur;

(b) 1/6 of the clear span of the member; and

(c) 45 cm.

Research results indicate that the length should be increased by 50 percent or

more in locations, such as the base of a building, where axial loads and

flexural demands may be especially high.

ACI 18.7.5.2 requires that the transverse reinforcement shall satisfy the

following:

184

(a) Transverse reinforcement shall comprise either single or overlapping

spirals, circular hoops, or rectilinear hoops, with or without crossties.

(b) Bends of rectilinear hoops and crossties shall engage peripheral

longitudinal reinforcing bars.

(c) Crossties of the same or smaller bar size as the hoops shall be permitted,

subject to limitations of 25.7.2.2 (column tie diameter). Consecutive

crossties shall be alternated end for end along the longitudinal

reinforcement and around the perimeter of the cross section.

(d) Where rectilinear hoops or crossties are used, they shall provide lateral

support to longitudinal reinforcement in accordance with 25.7.2.2 and

25.7.2.3 (column tie arrangement).

e) Reinforcement shall be arranged such that the spacing xh of longitudinal

bars laterally supported by the corner of a cross tie or hoop leg shall not

exceed 35 cm around the perimeter of the column.

f) Where cgu fAP 3.0 or 2/700 cmKgfc in columns with rectilinear

hoops, every longitudinal bar around the perimeter of the column core

shall have lateral support provided by the corner of a hoop or by a seismic

hook, and the value of xh shall not exceed 20 cm. uP shall be the largest

value in compression consistent with factored load combinations

including E.

Example of transverse reinforcement in columns

Spacing of transverse reinforcement along the length l of the member shall

not exceed the smallest of (a), (b) and (c):

185

(a) one-fourth of the minimum member dimension;

(b) six times the diameter of the smallest longitudinal bar

(c)

3

3510 xh

s , where s shall not exceed 15 cm and need not be

taken less than 10 cm.

Amount of transverse reinforcement shall be in accordance with Table

18.7.5.4. The concrete strength factor fk and confinement effectiveness

factor nk are calculated as shown below:

0.160.01750

cf

fk

2

l

ln

n

nk

where ln is the number of longitudinal bars around the perimeter of the

column core with rectilinear hoops that are laterally supported by the corner

of hoops or by seismic hooks.

where

ytf = yield stress of the transverse reinforcement

gA = gross cross-sectional area of concrete section

chA = cross-sectional area of a column measured to the outside edges of

transverse reinforcement.

186

s center-to-center spacing of transverse reinforcement measured along the

longitudinal axis of the column.

Expressions (a), (b), and (c) in Table 18.7.5.4 are to be satisfied in both

cross-sectional directions of the rectangular core. For each direction, cb is the

core dimension perpendicular to the tie legs that constitute shA , as shown in

Fig. R18.7.5.2.

Beyond the length l , the column shall contain spiral or hoop reinforcement

satisfying 25.7.2 through 25.7.4 (column ties/spirals) with center-to-center

spacing, s , not exceeding the lesser of six times the diameter of the smallest

longitudinal column bars and 15 cm, unless a greater amount of transverse

reinforcement is required by 18.7.5.2, 18.7.5.3, or 18.7.6 (shear strength) .

Columns supporting reactions from discontinued stiff members, such as

walls, shall satisfy (a) and (b):

(a) Transverse reinforcement required by 18.7.5.2 through 18.7.5.4 shall be

provided over the full height at all levels beneath the discontinuity if the

factored axial compressive force in these members, related to earthquake

effect, exceeds gc Af '1.0 . Where design forces have been magnified to

account for the over-strength of the vertical elements of the seismic-force-

resisting system, the limit of gc Af '1.0 shall be increased to gc Af '25.0 .

(b) Transverse reinforcement shall extend into the discontinued member at

least dl of the largest longitudinal column bar, where dl is determined in

accordance with ACI 18.8.5 (development length of bars in tension). Where

the lower end of the column terminates on a wall, the required transverse

reinforcement shall extend into the wall at least dl of the largest longitudinal

column bar at the point of termination. Where the column terminates on a

footing or mat, the required transverse reinforcement shall extend at least 30

cm into the footing or mat.

187

Confinement requirements at column ends

(a) Spiral hoop reinforcement

188

Confinement requirements at column ends

(b) Rectangular hoop reinforcement

Columns supporting discontinued stiff members

189

5- Shear Strength Requirements:

The design shear force, eV , is to be determined from consideration of

maximum forces that can be generated at the faces of the joint at each end of

the column. These joint forces shall be determined using the maximum

probable moment strengths, prM , of the column associated with the range of

factored axial loads, uP , acting on the column. The column shears need not

exceed those calculated from joint strengths based on the probable moment

strength prM of the beams framing into the joint. In no case shall eV be less

than the factored shear determined by analysis of the structure.

Transverse reinforcement over the length l given in 18.7.5.1, shall be

designed to resist shear assuming 0cV when both (a) and (b) occur:

i. The earthquake-induced shear force represents ½ or more of the maximum

required shear strength within l ;

ii. The factored axial compressive force, uP , including earthquake effects is

less than cg fA '05.0 .

Loading cases for design of shear reinforcement in columns of special

moment frames

190

Example (9):

For the column shown in the figure, check the requirements of ACI 18.7 in relation

to columns which are part of special moment frames.

Note that factored loads are: tons337Pu and tons4.84Mu .

Use 2c cm/Kg300'f and 2

y cm/Kg4200f .

Solution:

A- 18.7.2 "Dimensional limits":

Based on ACI 18.7.2.1, the shortest cross-sectional dimension, measured on

a straight line passing through the geometric centroid shall not be less than

30 cm. This requirement is satisfied since the shortest cross-sectional

dimension = 45 cm.

191

The ratio of the shortest cross-sectional dimension to the perpendicular

dimension shall not be less than 0.40.

Ratio = 40.064.070

45 (O.K)

B- ACI 18.7.3 "Minimum Flexural Strengths of Columns":

Based on ACI 18.7.3.2, the flexural strengths of the columns shall satisfy

the following equation:

nbnc MM 2.1

Considering the columns on both sides of the joint are of equal flexural

strengths, the flexural strength of each of the columns is determined using

nominal strength interaction diagrams.

01558.0g

, ksif c 4' ,

821.070

5.2124270

, tons337Pu

55.0457030065.0

1000337/

gc

nn

Af

PK

Using nominal load-moment strength interaction diagram, L4-

60.80, 165.0' hAf

M

gc

n and thereby mtMn .15.109

From example (8),

m.t35.41veMveM nlnr and mtveMveMnlnr

.82.59

mtMnc .30.21815.10915.109 , mtMnb .17.10182.5935.41

2.116.217.101

3.218

nb

nc

M

M (O.K)

192

C- ACI 18.7.4 "Longitudinal Reinforcement":

Based on ACI 18.7.4.1, the reinforcement ratio g shall not be less than 0.01

and shall not exceed 0.06.

01558.0

7045

087.49g (O.K)

Based on ACI 18.7.4.3, lap splices are only permitted within the center half

of the member length and shall be designed as tension lap splices enclosed

within transverse reinforcement in accordance with ACI 18.7.5.2 and

18.7.5.3.

Length of lap splice of longitudinal bars (in tension):

For Class "B" lap splice, dsp l3.1l

b

c

b

trb

sety

d d

fd

Kc

fl

'5.3

1t , 1e , 1s , and 1

bc = 4.0 + 1.0 + 1.25 = 6.25 cm

or

bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (8) = 4.0625 cm

i.e., bc is taken as 4.0625 cm

Ignoring the effect of transverse reinforcement, 0K tr

5.2625.15.2

00625.4

b

trb

d

Kc

59.1065.2300625.15.3

0.14200

dl

Required splice length cmlsp 57.13859.1063.1 , taken as 140 cm.

Based on ACI 18.7.5.3, transverse reinforcement shall be spaced at a distance

not exceeding (a) one-quarter of the minimum column dimension, (b) six

times the diameter of the smallest longitudinal bar, and (c)

3

3510 xh

s ,

where S is maximum longitudinal spacing of transverse reinforcement, shall

not exceed 15 cm and need not be taken less than 10 cm. In the same

193

expression xh is maximum horizontal spacing of hoop or crosstie legs on all

faces of the column.

Thus, mmaximum vertical spacing of transverse reinforcement is not to

exceed the smallest of :

i. 45/4 = 11.25 cm

ii. 6 (2.5) = 15 cm

iii.

3

3510 xh

s = 10 cm

cm5.30

2

14270h x

. Thus maximum spacing is limited to 10 cm

(based on the minimum of i, ii and iii).

Based on ACI 18.7.5.2 (e), the spacing xh of bars laterally supported by the

corner of a crosstie or hoop leg shall not exceed 35 cm around the perimeter

of the column.

Two cross ties are added to the existing mm10 hoops to satisfy this

requirement (maximum spacing of 35 cm).

Based on ACI 18.7.5.2 (f), column load =337 tons and tonstonsfA cg 33750.2831000/30070453.03.0

Therefore, xh shall not exceed 20 cm.

D- 18.7.5 "Transverse Reinforcement":

Based on ACI 18.7.5.4 (b), the total cross-sectional area of rectangular hoop

reinforcement shall be based on Table 18.7.5.4

For shear in the direction of shorter side of the column:

0.177.060.01750

300fk , taken as 1.0

25.18

10nk

2

2 96.416237

7045

4200

30062103.0cmAsh

2

'2 98.34200

300621009.0cmAsh

2

2 43.5621062374200

33700025.10.120.0 cmAsh

i.e., 2

2 43.5 cmAsh

Use mm12 tie plus three mm12 cross ties ( 265.5 cmAsh )

For shear in the direction of longer side of the column:

194

2

1 96.216237

7045

4200

30037103.0cmAsh

2

1 38.24200

300371009.0cmAsh

2

1 24.3371062374200

33700025.10.120.0 cmAsh

i.e., 2

1 24.3 cmAsh

Use mm12 tie plus three mm10 cross ties ( 2615.4 cmAsh )

Based on ACI 18.7.5.1, transverse reinforcement in amount specified before

shall be provided over a length l from each joint face and on both sides of

any section where flexural yielding is likely to occur as a result of inelastic

lateral displacements of the frame. The length l shall not be less than the

largest of:

(a) The depth of the member at the joint face = 70 cm

(b) 1/6 of the clear span of the member= 400/6 = 66.67 cm

(c) 45 cm.

i.e., l = 70 cm.

Based on ACI 18.7.5.5, where transverse reinforcement as specified before is

not provided throughout the full length of the column, the remainder of the

column length shall contain hoop reinforcement with center-to-center spacing

not exceeding the smaller of six times the diameter of the longitudinal

column bars or 15 cm.

Smax = the larger of 6 (2.5) cm and 15 cm = 15 cm

195

E- ACI 18.7.6 "Shear Strength Reinforcement":

The design shear force eV is to be determined from consideration of

maximum forces that can be generated at the faces of the joint at each end of

the column. These joint forces shall be determined using the maximum

probable moment strengths prM of the column associated with the range of

factored axial loads acting on the column. The column shears need not

exceed those determined from joint strengths based on the probable moment

strength prM of the beams framing into the joint. In no case shall eV be less

than the factored shear determined by analysis of the structure.

tonsVe 865.30

4

77.5069.7277.5069.722/1

(see Example 8 for prM

values)

cm55.6325.12.1470d

tons25.261000/55.634530053.0Vc (neglecting effect of axial force)

cns VVV and cu

s VV

V

196

tons90.1425.2675.0

865.30Vs

S

dfAV

yvs and

0558.055.634200

10009.14

df

V

S

A

y

sv

0558.00375.0

4200

455.3

S

A

min

v

(O.K)

For cmsS 15 , 2837.0 cmAv (satisfied at sections 1-1, 2-2 and 3-3).

197

B- Columns of Intermediate Moment Frames

Requirements of ACI 18.4.3 are applicable for columns of intermediate moment

frame columns forming part of the seismic-force resisting system.

1- Transverse Reinforcement:

At both ends of the column, hoops shall be provided at spacing s over a

length l measured from the joint face.

The length l shall not be less than the largest of:

(a) 1/6 of the clear span of the column

(b) Maximum cross-sectional dimension of the column

(c) 45 cm.

The spacing s shall not exceed the smallest of:

(a) 8 times the diameter of the smallest longitudinal column bar

(b) 24 diameter of the hoop bar

(c) One-half of the smallest cross-sectional dimension of the column

(d) 30 cm.

The first hoop shall be located not more than 2/s from the joint face.

Outside the length l , spacing of the transverse reinforcement shall conform

to ACI 10.7.6.5.2 (maximum spacing of shear reinforcement).

Columns supporting reactions from discontinuous stiff members, such as

walls, shall be provided with transverse reinforcement at the spacing s in

accordance with 18.4.3.3 over the full height beneath the level at which the

discontinuity occurs if the portion of factored axial compressive force in

these members related to earthquake effects exceeds gc Af '1.0 . If design

forces have been magnified to account for the overstrength of the vertical

elements of the seismic-force-resisting system, the limit of gc Af '1.0 shall be

increased to gc Af '25.0 . Transverse reinforcement shall extend above and

below the column in accordance with 18.7.5.6(b).

Columns shall be spirally reinforced in accordance with Chapter 10 or shall

be in accordance with 18.4.3.3 through 18.4.3.5, discussed in 1. Provision

18.4.3.6 shall apply to all columns supporting discontinuous stiff members

198

2- Shear Strength Requirements:

Design shear strength of columns nV resisting earthquake effect shall be at

least the lesser of (a) and (b):

(a) The shear associated with development of nominal moment

strengths of the column at each restrained end of the unsupported

length due to reverse curvature bending. Column flexural strength

shall be calculated for the factored axial force, consistent with the

direction of the lateral force considered, resulting in the highest

flexural strength.

(b) The maximum shear obtained from factored load combinations that

include E, with E substituted for E.

199

200

B- Columns of Ordinary Moment Frames

Requirements of ACI 18.3.3 are applicable to columns of ordinary moment frames

forming part of the seismic-force resisting system and classified as SDC "B".

Shear Strength Reinforcement:

Columns having unsupported length 15clu shall have at least the lesser of (a) and

(b):

(a) The shear associated with development of nominal moment strengths of the

column at each restrained end of the unsupported length due to reverse

curvature bending. Column flexural strength shall be calculated for the

factored axial force, consistent with the direction of the lateral forces

considered, resulting in the highest flexural strength.

(b) The maximum shear obtained from design load combinations that include E ,

with E substituted for E .