General Description of Example
The structure under consideration is a two-story planar wall with 6’ wide doorways centered horizontally on the wall. No other structural elements (slabs, beams, columns, etc.) are considered, so that the wall design can be isolated. The stories are 12’-6” high and the walls are 12” thick.
The design is in accordance with ACI 318-08, and is categorized as an ordinary reinforced concrete structural wall per Section 21.1.1.7. Thus no provisions of Chapter 21, Earthquake-Resistant Structures, need to be fulfilled. The coupling beam under consideration is at the 2nd level.
Figure 1 - Elevation view of wall system
Materials
- f’c = 5,000 psi
- fy = 60 ksi
Dimensions
Coupling beam dimensions are as follows:
- h = 72”
- bw = 12”
- Ln = 72”
Reinforcing
Coupling beam reinforced for flexure with a uniform mat of longitudinal bars, consisting of #6@12” o.c. at each face of wall.
Coupling beam reinforced for shear with #4 stirrups at 12” along entire span.
Figure 2 - Cross section view of coupling beam at second level
Ag = 72” x 12” = 864 in2
As = 7 x 2 x 0.44 = 6.16 in2
1.5” clear cover top and bottom
d = 0.8 x 72” = 57.6”
Applied Loads
A vertical point load is applied at midspan of the coupling beam at each story, 150 kips dead and 75 kips live. No other gravity loads are considered (self-weight is turned off in RAM model).
Lateral loads are applied at each story solely to generate compression or tension force within coupling beams, in order to demonstrate the effects of compression and tension on shear strength calculations. These loads are categorized as wind loads to keep them separate from gravity cases.
Figure 3 - Applied dead, live, and wind loads
Coupling Beam Design Forces
The forces in the coupling beam can be retrieved in RAM Frame using the shear wall forces module. A section is drawn at each end of the coupling beam span (inset 3” from the face) and at midspan. There is a dead, live, and wind load case.
Only one load combination is considered for this example:
1.2D + 0.5L + W
In this case the coupling beam is in compression.
Axial
- PD = 25.79 k (tension)
- PL = 12.89 k (tension)
- PW = 84.56 k (compression)
Shear (at span ends):
- VD = 74.76 k
- VL = 37.38 k
- VW = 0.00 k
Moment (positive flexure at midspan):
- MD = 163.13 k-ft
- ML = 81.57 k-ft
- MW = 8.16 k-ft
Figure 4 - Forces at critical sections in coupling beam in RAM Frame
Shear Design
Pu = 1.2x(-25.79) + 0.5x(-12.89) + 84.56 = 47.17 k (compression)
Vu = 108.40 k
Mu = 244.70 k-ft (positive flexure at midspan)
Concrete shear strength for members subjected to axial compression, Equation (11-4):
Steel shear strength per section 11.4.7.2, Equation (11-15):
> Vu = 108.40 k
Figure 5 - Shear design results in RAM Concrete View/Update dialog - compression case
Maximum shear strength per 11.4.7.9:
OK
Maximum flexural bar spacing per section 7.6.5:
s <= 18" OK
Stirrup spacing limit per section 11.4.5.1:
s <= d/2 = 57.6"/2 = 28.8" OK
Check of limit 11.4.5.3:
OK
Minimum area of shear reinforcement per section 11.4.6.3, Equation (11-13):
OK
Case of Tension in Coupling Beam
Now the same calculations will be run for the load combination:
1.2D + 0.5L - W
In this case the coupling beam is in tension.
Shear Design
Pu = 1.2x(-25.79) + 0.5x(-12.89) - 84.56 = -121.95 k (tension)
Vu = 108.40 k
Mu = 244.70 k-ft (positive flexure at midspan)
Concrete shear strength for members subject to significant axial tension per section 11.2.2.3, Equation (11-8):
= 2 x (1 - 0.2823) x 48,875.2 = 70.16 k
Steel shear strength per section 11.4.7.2, Equation (11-15):
> Vu = 108.40 k
Figure 6 - Shear design results in RAM Concrete View/Update dialog - tension case