Strength Interaction Diagram by Spreadsheet

CMU Masonry Shear Wall - Example Problem 20.4

f'm=1500 psi, 24.67 ft long, 7.625 in. thick,#5 bars @ 4' spacing
5000

4000

fPn, kips

3000

2000

1000

0
0

2000

4000

6000

-1000
fMn, ft-kips

8000

10000

12000

Spreadsheet for calculating strength moment-axial force interaction diagram for concrete masonry shear wall
depth, d v

e mu

216 in.

h=

180 in.

height

0.0025

f' m

2.5 ksi

s=

34.67 in.

bar spacing

fy

60 ksi

h/r =

53.64

slenderness ratio

Es
d1

29000 ksi

(c/d) balanced
width (wall thickness) t sp

212 in.
0.5472

Input axial load and mo

11.625 in.

Pu =
Mu =

0.9
m =
1.5
cmax/d = 0.4462
c max =
94.58461538 in.
steel layers are counted from the extreme compression fiber to the extreme tension fiber
distances are measured from the extreme compression fiber
reinforcement is assumed to be placed at 4-ft intervals
compression in masonry and reinforcement is taken as positive
stress in compressive reinforcement is set to zero, because the reinforcement is not laterally supported (except in determining

Row of Reinforcement
7
6
5
4
3
2
1

pure axial load

Points controlled by masonry

Points controlled by masonry

Points controlled by steel

distance from
extreme
compression
fiber, di
4.00
38.67
73.33
108.00
142.67
177.33
212.00

Area
1.00
1.00
1.00
1.00
1.00
1.00
1.00

c/d 1

1.0137
0.9
0.8
0.7
0.6
0.5472
0.5472
0.5
0.4
0.3
0.2
0.1
0.01

214.90
190.80
169.60
148.40
127.20
116.00
116.00
106.00
84.80
63.60
42.40
21.20
2.12

Slenderness factor
R=
0.8532

area
s, in.
As/cell, in2

Cmasonry

f s7

f s6

f s5

3997.22
0.00
0.00
0.00
3548.88
0.00
0.00
0.00
3154.56
0.00
0.00
0.00
2760.24
0.00
0.00
0.00
2365.92
0.00
0.00
0.00
2157.60
0.00
0.00
0.00
2157.60
0.00
0.00
0.00
1971.60
0.00
0.00
0.00
1577.28
0.00
0.00
0.00
1182.96
0.00
0.00 -11.10
788.64
0.00
0.00 -52.89
394.32
0.00 -59.73 -60.00
39.43 -60.00 -60.00 -60.00

f s4
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-1.37
-19.83
-50.61
-60.00
-60.00
-60.00

f s3
0.00
0.00
0.00
0.00
-8.82
-16.67
-16.67
-25.08
-49.47
-60.00
-60.00
-60.00
-60.00

f * Pure tension = - sum (Asify)

Pure tension = - sum (Asify)

f Pn,max
Code Eqn. 3-18 or 3-19
D + 0.75L + 0.525QE

rt =

c = cmax

94.58

276 kips

0.002787734

1759.27 60.00

42.86 16.29 -10.28

f * Code Eqn. 3-18 or 3-19

-36.86

Input axial load and moment for up to 5 load combinations

800

kips

8000

kip-ft

ted (except in determining P max)

8.00
0.23

area of steel in each reinforced cell

40
48
16.00 24
32.00
0.46 0.69
0.92
1.15
1.38

56
1.62

64
1.85

f M n , k-ft
f P n , kips
f s2
0.00
0.00
-3.31
-14.14
-28.57
-38.33
-38.33
-48.79
-60.00
-60.00
-60.00
-60.00
-60.00

f s1 Moment
Axial Force
0 4507
0.00 6607 3597
-8.06 8495 3187
-18.13 9660 2820
-31.07 10385 2444
-48.33 10684 2052
-60.00 10679 1838
-60.00 10679 1838
-60.00 10487 1653
-60.00 9672 1249
-60.00 8232
847
-60.00 6183
446
-60.00 3413
31
-60.00 317
-343

f M n /f' m tfspPdnv/f'2 m t sp d v
0
0.0049
0.0063
0.0071
0.0077
0.0079
0.0079
0.0079
0.0077
0.0071
0.0061
0.0046
0.0025
0.0002

0.718
0.573
0.508
0.449
0.389
0.327
0.293
0.293
0.263
0.199
0.135
0.071
0.005
-0.05

Asify)

-19

-378
=540.2
-60.00 -60.00 f Pn,max1
0 2769
10684 2769

-0.06
0.8
0.7
0.6
0.5
0.4
0.3

Series1

0.2
0.1
0
-0.005

-0.1
-0.2

0.005

0.01

Shear design for shear walls

M u
Vnm 4.0 1.75
An
V
d

u v

f'm =
Mu =

f m ' 0.25 Pu

2500 psi
120000 k-in

Pu =

50 k

Vu =
l=
dv =
t=
An =

260
248
248
7.625
1891

Mu/Vudv =

1.861

Mu/Vudv =

k
in (wall length)
in (same as wall length)
in, actual, not nominal, wall thickness
in2

Vnm =
shear coef =
=
Vn,max =

225.24 k
1.70388751
4
378.2 Vu

phi shear =
Vns =

99.7625

fy =

60000

Av/s =

0.013408938

< Vn,max - OK

0.8

Provisions for Special Shearwalls

Mn =
140000 k-in - nominal moment capacity (from Shearwall Calculations Worksheet)
1.25Mn =
Vu =
Mu, top =

175000 nominal capacity

379.17 kips, scaled up
88800 k-in

Mu/Vudv =

1.861

Mu/Vudv =

Mtop =
Vnm =
height, H =

129500 k-in - scaled up

225.24 k
120 in

fVn = (1.25Mn Mtop)/h1

=
=
Vns =
Av/s =
scale factor =

379.17
379.17 Exceeds V n,max, increase masonry area or f'm
153.9
0.020689404
1.458333333
0
175000

This Worksheet is for strength design of masonry walls for combined out of plane moment and axial load, i
Enter the values in the yellow cells. The software iterates the deflections through 12 cycles. If the design un
After calculating the addional moment due to P - D, the spreadsheet calculates the required steel area.
The required steel area (Cell M36) should be < the assumed steel area (Cell H16). If not, repeat the design
Other code checks are also made
This includes updates for inclusion of axial load stress added to f r to calculate Mcr.
It also uses the new equation for Icr (3-31 and 3-32)

nominal wall thk, in

ksi
Steel area in each reinforced cell, in2

t=
f'm =

8
2.5

8
2.5

8
2.5

8
2.5

As = 0.310000
0.31
0.31
0.31
fy =
ksi
60
60
60
60
bar spacing, in
s=
24
24
24
24
np = 0.043667
n=
12.89
As = 0.155000
k = 0.255066
Icr = 19.79227 not used
d=
3.8125
d=
3.8125 in.
modulus of rupture, fr =
153 psi, table 3.1.8.2.1
4
c = 0.524219 in. Icr = 23.95469 in , from ACI 530 Code Eqns. 3-31

Pu, lb/ft
h, ft.
Mu, in-lb/ft
P-D

765
765
765
765
765
24
24
24
24
24
29720.7 29881.06 29900.73 29903.14 29903.44

Mcr, in-lb/ft

18763.22 18763.22 18763.22 18763.22 18763.22 18763.22

Icr, in

23.95469 23.95469 23.95469 23.95469 23.95469 23.95469

Ig, in4

443.3223 443.3223 443.3223 443.3223 443.3223 443.3223

Em, psi

2250000

du, in
dMu, in-lb/ft

1.70941 1.919037 1.944744 1.947897 1.948283 1.948331

Ase=(Asfy + Pn)/fy =
a = (Asfy + Pn)/(.8f'mb) =
Ase=Mu/ffy(d-a/2) =
As = Ase - Pu/fy =
Iterative method to
solve for required
steel area

765
24
28413

a=
Ase =
As =
cmax =
As-max =
0.05f'mAn =
Pmax =

2250000

2250000

2250000

2250000

2250000

29720.7 29881.06 29900.73 29903.14 29903.44 29903.47

2
0.169 in
Mn = Asefy (d - a/2)=

0.423 in
2
0.154 in
2
0.141 in

Mu = fMn = 32.89552 k-in

0.384 0.382407
0.1530
0.1529
0.139

36.55057 k-in

0.3823 0.382294 0.382294 0.382294

0.1529
0.1529
0.1529
0.1529

0.139

0.139

0.139

0.139

0.139

1.701 in
2
0.532 in

this area exceeds the actual area usedOK

11.4375 kips

Code Section 3.3.5.3

23.358 21.02262 kips

Pmax = 41.90353 37.71318 kips

Code Section 3.3.3.5 (ductility requirement)

Code Eqns. 3-18 or 3-19 (Slenderness)

out of plane moment and axial load, including the P -D effect.

ns through 12 cycles. If the design unstable, the iterations will not converge.
alculates the required steel area.
a (Cell H16). If not, repeat the design with a larger assumed steel area (larger bar or smaller spacing).

alculate Mcr.

8
2.5

8
2.5

8
2.5

8
2.5

8
2.5

8
2.5

0.31

0.31

0.31

0.31

0.31

0.31

60
24

60
24

60
24

60
24

60
24

60
24

130.84

R=

0.286

in2/ft
in.
h/r =

in4, from ACI 530 Code Eqns. 3-31 and 3-32

765
24
29903.47

765
24
29903.48

765
765
765
765
24
24
24
24
29903.478 29903.48 29903.48 29903.48

18763.22

18763.22

18763.219 18763.22 18763.22 18763.22

23.95469

23.95469

23.954693 23.95469 23.95469 23.95469

443.3223

443.3223

443.32227 443.3223 443.3223 443.3223

2250000

2250000

1.948336

1.948337

1.9483372 1.948337 1.948337 1.948337

29903.48

29903.48

29903.478 29903.48 29903.48 29903.48 in-lb

2250000

2250000

2250000

2250000

design moment including the P - D effect (AC

moment capacity of the wall based on input steel size and spacing

0.382294
0.1529

0.382294
0.1529

0.139

0.139

(ductility requirement)

19 (Slenderness)

0.3822936 0.382294 0.382294 in

2
0.1529
0.1529
0.1529 in
2
0.139
0.139
0.139 in

this is less than the value of As used to calculate Icr, so

0.277502 area per grouted cell

ment including the P - D effect (ACI 530 Code eqn. 3-26)

lue of As used to calculate Icr, so OK