A u t

®
Autodesk
™
Robot Structural Analysis
Professional
VERIFICATION MANUAL
FOR ITALIAN CODES
March 2014
Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
INTRODUCTION ..............................................................................................................................................................................1
CONCRETE .....................................................................................................................................................................................2
1. DM 9/1/96 – RC COLUMNS.........................................................................................................................................................3
VERIFICATION EXAMPLE 1 - COLUMN SUBJECTED TO AXIAL LOAD AND BIAXIAL BENDING ..............................................................4
LITERATURE .............................................................................................................................................................................10
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
INTRODUCTION
This verification manual contains numerical examples for RC columns prepared and calculated by
Autodesk Robot Structural Analysis Professional version 2013. The comparison of results is still
valid for the next versions.
All examples have been taken from handbooks that include benchmark tests covering fundamental
types of behaviour encountered in structural analysis. Benchmark results (signed as “Handbook”) are
recalled, and compared with results of Autodesk Robot Structural Analysis Professional (signed further
as “Robot”).
Each problem contains the following parts:
- title of the problem
- specification of the problem
- Robot solution of the problem
- outputs with calculation results and calculation notes
- comparison between Robot results and exact solution
- conclusions.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
CONCRETE
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
1. DM 9/1/96 – RC columns
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
VERIFICATION EXAMPLE 1
- Column subjected to axial load and biaxial bending
DESCRIPTION OF THE EXAMPLE:
Following example illustrates the procedure of dimensioning of biaxial bending of column, which is
non-sway in one direction, whereas sway in the other. The results of the program are accompanied by
the „manual‟ calculations.
1.
SECTION DIMENSIONS
2.
MATERIALS
Concrete
Longitudinal reinforcement
Transversal reinforcement
3.
: R20
: FeB44k
: FeB32k
Rck = 24.10 (MPa)
fyk = 430.00 (MPa)
fyk = 315.00 (MPa)
BUCKLING MODEL
As can be seen the sway column is assumed for Z direction, and the non-sway column for Y direction.
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
4.
LOADS
NOTE: Let us assume, the moments in Y direction are linearly distributed along the height of the
column. Thus, we define only the ends‟ moments for Y direction. In Z direction however, we assume
the mid-height moment is not a result of the linear distribution. For such a case, Robot let the user
define the moments in the mid-section explicitly.
5.
CALCULATED REINFORCEMENT:
Program generates the reinforcement 20  16.
6.
RESULTS OF THE SECTION CALCULATIONS:
The dimensioning combination is 1.4DL1+1.0LL1
The dimensioning section (where the most unfavorable set of forces is found) is for that combination
the section in the mid-height of the column (marked as (C)).
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
Since the column is found as slender, the second-order effects are taken into account in both
directions.
In parallel the other sections (at the ends of the column) are checked for all combinations of loads.
In the top and bottom ends‟ sections of the column in Y direction, the influence of buckling has not
been taken into account, since the structure is non-sway in this direction. In Z direction however, the
influence of slenderness is taken into account for all three sections of the column.
All the results of total forces for each combination and each section of the column may be seen in the
table “Intersection” at the Column-results layout.
7.
CALCULATIONS OF TOTAL MOMENT:
7.1. LOADS
For the dimensioning combination, the loads are:
DL1
LL1
N
(kN)
400
150
MyA
(kN*m)
150
120
MyB
(kN*m)
30
30
MyC
(kN*m)
102
84
MzA
(kN*m)
20
10
MzB
(kN*m)
30
20
MzC
(kN*m)
50*
40*
1.4DL1+1.0LL1
710
330
72
226.8
38
62
110
Case
1
2
Dimensioning
combination
where A, B and C denote upper, lower and mid-height sections of the column respectively.
* - the values are written “by hand” by the user (see point 4 – Loads)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
7.2. THE INFLUENCE OF SLENDERNESS
Two independent calculations of the total moment for both directions are carried out.
As a first step, it is checked, if N d  N max (according to point 4.2.1.2.a)
f cd
 Ac  f yd  A  3863.68 (kN)
1.25
N d  710  3864  N max
- OK
N max 
Y DIRECTION
Slenderness analysis:

l0
= 46.19
i
Check if
   * according to 4.2.4.2.
1  15  
= 43.65
Nd / Ac
A
  s = 1.68 %
Ac
Ac = 0.24 m2
*  60 
Since
   * the column is found as slender for Y direction.
The abovementioned slenderness means that the total eccentricity of the axial force in Z
( c z  M y / N ) direction will be:
ctot  c'ca  
NOTE: If the column is found as non-slender (    * ), the total eccentricity would be ctot  c'ca .
Check if the method of slenderness analysis is applicable ( 
  46.19  130.95  3 *
 3 * )
- OK
Calculation of initial eccentricity c’
For the mid-height section, we have:
c'  0.4  c1  0.6  c2 = 0.319 (m) > 0.4  c2 = 0.186 (m)
Calculation of additional eccentricity ca
l 

c a  max  2cm; 0  = 0.027 (m),
300 

l0 = 8.0 (m)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
Calculation of second-order eccentricity 
2
l 1
= 0.055 (m)
 0
10 r
1
1
 K r K  = 0.00861
r
r0
f yd
1

= 0.0075
r0 0.45  d  E s
d = 0.554 (m)
Es = 200 (GPa)
f yd = 374 (MPa)
K  max(1;1    eff )
eff 
N long
N tot
  0.35

>2 and
  75 and c'  h

f ck


200 150
K  1
- in other cases
Thus, we have
Kr 
- if creep coefficient
K  1
N ud  N d
= 1.181
N ud  N bal
N ud  f cd  Ac  f yd  A = 4503.59 (kN)
N bal  0.4 f cd  Ac = 1200.00 (kN)
The total eccentricity in Z direction:
ctot  c'ca   = 0.401 (m)
The total moment My :
M y  N  etot  285 (kNm)
Z DIRECTION
Slenderness analysis:

l0
= 45.03
i
Check if
   * according to 4.2.4.2.
*  60 
1  15  
= 43.65
Nd / Ac
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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes

As
= 1.68 %
Ac
Ac = 0.24 m2
Since
   * the column is found as slender for Z direction.
The abovementioned slenderness means that the total eccentricity of the axial force in Y
( c y  M z / N ) direction will be:
ctot  c'ca  
NOTE: If the column is found as non-slender (    * ), the total eccentricity would be ctot  c'ca .
Check if the method of slenderness analysis is applicable ( 
  45.03  130.95  3 *
 3 * )
- OK
Calculation of initial eccentricity c’
For the mid-height section, we have:
c' M z (C ) / N d = 0.155 (m) (the moment in mid-height section is given directly by the user)
Calculation of additional eccentricity ca
l 

c a  max  2cm; 0  = 0.020 (m),
300 

l0 = 5.2 (m)
Calculation of second-order eccentricity 
2
l 1
 0
= 0.036 (m)
10 r
1
1
 K r K  = 0.01348
r
r0
f yd
1

= 0.0117
r0 0.45  d  E s
d = 0.354 (m)
Es = 200 (GPa)
f yd = 374 (MPa)
K  max(1;1    eff )
eff 
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N long
N tot
- if creep coefficient

>2 and
  75 and c'  h

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Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes
  0.35
f ck


200 150
K  1
- in other cases
Thus, we have
Kr 
K  1
N ud  N d
= 1.1483
N ud  N bal
N ud  f cd  Ac  f yd  A = 4503.59 (kN)
N bal  0.4 f cd  Ac = 1200.00 (kN)
The total eccentricity in Z direction:
ctot  c'ca   = 0.211 (m)
The total moment My :
M z  N  etot  150 (kNm)
7.3. FINAL RESULT
M y = 285 (kNm)
M z = 150 (kNm)
8.
CONCLUSIONS
The algorithm of calculations of the total moments (i.e. slenderness effects) in non-sway/sway column
has been presented. The results obtained with the program (see point 6 – Results of the Section
Calculations) are in agreement with the manual calculations (see point 7.3 – Final Result).
LITERATURE
[1] B.A.E.L. 91. Règles techniques de conception et de calcul des ouvrages et constructions en béton
armé suivant la méthode des états-limites. Mod. 99.
[2] J. Perchat, “Pratique du BAEL 91”, Deuxième èdition, Eyrolles, 1998, Example 2, pp. 98
[3] J-P. Mougin, “Béton Armé. BAEL 91 et DTU associés”, Eyrolles, 1995, Example 1, pp. 113
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