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# Re: Biaxial bending of a concrete beam

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Biaxial bending of a concrete beam
• From: TJ Fu <tzujfu(--nospam--at)gmail.com>
• Date: Mon, 10 Jan 2011 17:51:40 -0500

Mike,

Thanks for sending 11 pages of your “R.C. Column in Biaxial Bending Program” write-up to me. I have reviewed it and it is pretty good.  The example on last 3 pages clearly shows the design procedures in dealing with biaxial bending of a concrete beam.  I could check and followed most of your numbers easily.

I have a few comments, just for your reference.

PAGE 9:

·         To begin with, you assumed Ang. = 45-deg and c = 27.46”. I believe these assumed values have to be adjusted later based on the actual applied loads (Pu, Mux & Muy).

·         You used Es = 30,000 ksi.  ACI 8.5.2 suggests 29,000 ksi though.

PAGE 11:

·         In Table 7, I had a hard time figuring out the meanings of J0, J1, J2, J3, J4, A0 and B0.  The final results appear okay to me though.

·         In Table 8, Bar #2 Force = 24.16 kips.  Don’t you think it should be 1.27 in^2 x (20.47 ksi – 4.25 ksi) = 20.60 kips?  Same thing for Bar #5, 1.27 in^2 x (43.65 ksi – 4.25 ksi) = 50.04 kips instead of 51.51 kips?

·         You used 0.65 reduction factor.  The maximum rebar strain is 0.0024 in/in (Bar #3, Table 8).  Since it is more than 0.0020 (ACI 9.3.2.2 & 10.3.3), don’t you think it can be increased to 0.683 [= 0.65 + (0.0024 – 0.002) / (0.005 – 0.002)]?

·         The final results: Pn = 1993.4 kips;  Mnx = 674.2 k-ft;  Mny = 260.6 k-ft.  Rotation Angle = atan(Mnx / Mny) = 68.867 deg.  Should we readjust the assumed angle of 45 deg until they are equal?

·         Eccentricity: ey = Mnx / Pn = 0.338’ and ex = Mny / Pn = 0.131’.  e = (ex^2 + ey^2)^0.5 = 0.362’

·         Resistance Moment from concrete and rebars,  Mr = (Mnx^2 + Mny^2)^0.5 = 722.8 k-ft.

·         Applied Moment from Pn, Mn = Pn [e + 9.94” (Figure 9) / 12] = 2373 k-ft.  Should we adjusted assumed c value until Mr = Mn?

Normally, we know the applied loads Pu, Mux and Muy.  In my Mathcad files, I set the rotation angle = atan(Mux / Muy).  Then, the c value can be assumed/adjusted until Mr = Mn à  Pn value determined!  If Reduction Factor x Pn is => Pu, we are OK.  Otherwise, add more rebars to the section.

TJ Fu, P.E.

On Sat, Jan 8, 2011 at 3:40 AM, Michael Brooks wrote:
Hi Thomas,

The concrete section solver we use in ENERCALC's concrete modules is general
in nature and can handle any shape and rebar orientation.
I've got a good 11 page synopsis with example that describes the process
using Greene's Theorem for an exact solution.

The example is for a simple rectangular section rotated at 45 degrees and
may be just what you are looking for.

Please email me directly and I can send the PDF. support(--nospam--at)enercalc.com

Sincerely,

Michael D. Brooks, P.E., S.E.
ENERCALC, INC.

________________________________________
To: seaint(--nospam--at)seaint.org
Subject: Biaxial bending of a concrete beam
Date: Wed, 5 Jan 2011 16:20:03 -0800
Hi,

Does anyone know a good example or any reference material that clearly shows
the calculation of a concrete beam with biaxial bending?

Sincerely,

Thomas Kennedy, P.E.

3463 Oceanview Blvd
Glendale CA 91208
PH:818-249-8400
Fax: 818-249-8405

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