Evo Design - structural engineering Calculation No.
001-RC Column
CALCULATION SHEET Project No.
onlinestructuraldesign.com SAMPLE CALCULATION
Project Title: Reinforced Concrete Column - interactive design spreadsheet   Calc. By Date Rev.
MN 16.04.2014 0
Subject RC Column - M-N interaction diagram (EC2)   Checked By Date
CN 16.04.2014

InputÂ  Output
Column dimensions Moment capacity
Reinforcement
Materials (steel, concrete, bolts)

RC Column - Axial Force - Bending Moment Interaction per EN 1992-1-1:2004*
Axial force - bending moment interaction -Â  ultimate limit state Section 3 Column dimensions
bx = 300 mm (parameters that can not be
bz = 300 mm modified in the demo version)
Ap = mm2 (Element area = bx * by)

Reinforcement
c = mm cover
d = mm (bx - c)

Tension side reinforcement
f =Â  mm bars diameter
n =   no of bars
As.a = mm2 area of tension reinforcement
preinf.a = % percentage of tension reinforcement

Compression side reinforcement
f =Â  mm bars diameter
n =   no of bars
As.b = mm2 area of compression reinforcement
preinf.b = % percentage of compression reinforcement
preinf.a+b = % element percentage of reinforcement

Materials
Concrete class
per EN 1992-1-1:2004
fck = MPa concrete characteristicÂ  Section 3 Table 3.1
cylinder strength
Reinforcement type
see reinforcement types here
fyk = MPa reinforcement yield strength

Partial factors for materials for ultimate limit states per EN 1992-1-1:2004
Section 2 Table 2.1N
gc =   values for Persistent & Transient design situations
gs =   recommended by the Eurocode; values to be used
may be found in the Eurocode National Annexes
Design compressive concrete strength per EN 1992-1-1:2004
Section 3.1.6 & Formula 3.15
acc =             Coefficient taking account of long term effects
fcd = acc * fck / gc = MPa on the compressive strength and of unfavourable
effectsresulting from the way the load is applied
value may be found in the EC National Annex
References:
EN 1993-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings

Calculation No.

CALCULATION SHEET Project No.
onlinestructuraldesign.com
Project Title:   Calc. By Date Rev.

Subject   Ckd. By Date

Ultimate concrete compressive shortening strain
ecu3 = per EN 1992-1-1:2004
1000 Section 3.1.3 Table 3.1

per EN 1992-1-1:2004
Section 3.1.7 (2) Figure 3.4
Bi-linear stress-strain relation

Design reinforcement strength
fyd = fyk / gs   = MPa per EN 1992-1-1:2004
Section 3.1.7 Figure 3.8
Reinforcement ductility class

ductility class A, B or C
defining reinf. strain at maximum force
Characteristic reinf. strain at maximum force
euk =   per EN 1992-1-1:2004
100 Annex C - Table C1
function of reinf. ductility class
Design reinf. strain at maximum force
eud = * euk = % per EN 1992-1-1:2004
Section 3.2.7 Note 1
The value of eud for use in a Country may be
found in its National Annex.
Â The recommended value is 0.9*euk
Reinforcement modulus of elasticity per EN 1992-1-1:2004
Es = 200 GPa Section 3.2.7 (4)
The design value of the modulus of elasticity
Es may be assumed to be 200 GPa
Stress strain relations for the design of cross-section per EN 1992-1-1:2004
Section 3.1.7 (3)
A rectangular stress distribution is assumed
l, defining the effective height of the compression
zone and h, defining the effective strength are
derived from formulas 3.19, 3.20, 3.21 and 3.22

l =
h =

Calculation No.

CALCULATION SHEET Project No.
onlinestructuraldesign.com
Project Title:   Calc. By Date Rev.

Subject   Ckd. By Date

Points defining the axial force - bending moment interaction diagram
Case 0 The entire section is in tension
Fs.a = - As.a * fyd = kN     Reinforcement has yielded.
Fs.b = - As.b * fyd = kN     Concrete tensile capacity is ignored.
Ncap = Fs.a + Fs.b = kN
Mcap = Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)
Mcap = kN*m

Case 1
Concrete strain: ecu3     Concrete has reached ultimate concrete design
Tension reinforcement strain: es.a = eud compressive shortening strain andÂ  reinforcement
x1 =Â  ecu3 * d / (-es.a + ecu3) = mm     has reached design reinforcement strain
a1 =Â  l * x1 = mm
Fb = h * a1 * bz * fcd = kN
Fs.a = -As.a * fyd = kN
es.b = ecu3 * (x1 - c) / x1 = /1000   Compression side reinforcement strain
fyd/Es = /1000 Reinforcement yield strain

Fs.b = Â - fyd * As.b compression side reinforcement is in tension and it has yielded
Fs.b = Â - Es * es.b * As.b compression side reinforcement is in tension and has not reached yield point
Fs.b = Â + fyd * As.b compression side reinforcement is in compression and it has yielded
Fs.b = Â + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point

Fs.b = kN

Ncap = Fb + Fs.a + Fs.b = kN
Mcap = Fb * (bx - a1)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)
Mcap = kN*m

Case 2 Concrete has reached ultimate concrete design
Concrete strain: ecu3   Â compressive shortening strain andÂ  reinforcement
Tension reinforcement strain: es.a = -fyd / Es has reached yield reinforcement strain
fyd/Es = /1000

x2 =Â  ecu3 * d / (-es.a + ecu3) = mm
a2 =Â  l * x2 = mm
Fb = h * a2 * bz * fcd = kN
Fs.a = -As.a * fyd = kN
es.b = ecu3 * (x2 - c) / x2 = /1000 Compression reinforcement strain
fyd/Es = /1000 Reinforcement yield strain

Fs.b = Â - fyd * As.b compression side reinforcement is in tension and it has yielded
Â - Es * es.b * As.b compression side reinforcement is in tension and has not reached yield point
Â + fyd * As.b compression side reinforcement is in compression and it has yielded
Â + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point

Fs.b = kN

Ncap = Fb + Fs.a + Fs.b = kN
Mcap = Fb * (bx - a2)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)
Mcap = kN*m

Calculation No.

CALCULATION SHEET Project No.
onlinestructuraldesign.com
Project Title:   Calc. By Date Rev.

Subject   Ckd. By Date Rev.

Case 3 Concrete has reached ultimate concrete design
Concrete strain: ecu3 Â compressive shortening strain andÂ  the height
The entire section is in compression x3 =Â  bx = mm of the compressed zone is equal with the section height

a3 =Â  l * x3 = mm
Fb = h * a3 * bz * fcd = kN
es.b = ecu3 * (x3 - c) / x3 = /1000     Compression side reinforcement strain
es.a = ecu3 * (x3 - d) / x3 = /1000     Tension side reinforcement strain
fyd/Es = /1000           Reinforcement yield strain

Compression side reinf. is in compression
Fs.b = Â + fyd * As.b compression side reinforcement is in compression and it has yielded
Fs.b = Â + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point
Fs.b = kN

Tension side reinf. is in compression
Fs.a = Â + fyd * As.a compression side reinforcement is in compression and it has yielded
Fs.a = Â + Es * es.a * As.a compression side reinforcement is in compression and has not reached yield point
Fs.a = kN
Ncap = Fb + Fs.a + Fs.b = kN
Mcap = Fb * (bx - a3)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)
Mcap = kN*m

Case 4 The entire section is in compression,
Concrete strain: ecu3 concrete has reached ultimate concrete design
The entire section is in compression es.b = es.a = ecu3     compressive shortening strain andÂ  reinforcement
is in compresiion
fyd/Es = /1000 Reinforcement yield strain
Fb = h * bx * bz * fcd = kN

Compression side reinf. is in compression
Fs.b = Â + fyd * As.b compression side reinforcement is in compression and it has yielded
Fs.b = Â + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point

Fs.b = kN

Tension side reinf. is in compression
Fs.a = Â + fyd * As.a compression side reinforcement is in compression and it has yielded
Fs.a = Â + Es * es.a * As.a compression side reinforcement is in compression and has not reached yield point

Fs.a = kN
Ncap = Fb + Fs.a + Fs.b = kN
Mcap = Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)
Mcap =
 kN*m

Data for the M-N interaction graph:

Ncap Mcap
kN kN*m
Case 0
Case 1
Case 2
Case 3
Case 4

Neff Meff
kN kN*m
CO1
CO2
CO3