A u t o

®
Autodesk
™
Robot Structural Analysis
Professional
VERIFICATION MANUAL
FOR SPANISH CODES
March 2014
Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish Codes
INTRODUCTION ..............................................................................................................................................................................1
CONCRETE .....................................................................................................................................................................................2
1. EHE 99 – 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 Spanish Codes
INTRODUCTION
This verification manual contains numerical examples for structures prepared and originally 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 Spanish Codes
CONCRETE
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Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish Codes
1. EHE 99 – RC columns
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Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish 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
: HA - 30
Longitudinal reinforcement: : B 500 S
Transversal reinforcement: : B 500 S
3.
fck = 30.00 (MPa)
fyk = 500.00 (MPa)
fyk = 500.00 (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 Spanish 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 12  32.
6.
RESULTS OF THE SECTION CALCULATIONS:
The dimensioning combination is 1.35DL1+1.5 LL1
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 Spanish Codes
Since the column is found as slender, in both direction the second-order effects are taken into
account.
In parallel the other sections (at the ends of the column) are checked for all combinations of loads.
NOTE: The second-order effects in Robot are taken into account dependent upon the section
and upon the parameter sway/non sway in a following way:
 in non-sway structures, M2f is added for the mid-height section only.
 in sway structures, M2f is added to each of three sections of column. Such addition is
carried out disregarding the distribution of the first-order moment.
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*
1.35DL1+1.5LL1
765
382.5
85.5
263.7
70.5
42
127.5
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 Spanish Codes
7.2. THE INFLUENCE OF SLENDERNESS
Two independent calculations of the total moment for both directions are carried out.
Y DIRECTION
Slenderness analysis
Geometrical Slenderness

l0
= 72.05
i
The slenderness limit:
lim  35
  lim
- the column is slender for Y direction
Calculation of minimal eccentricity – 12.2.3
emin  max( 0.02;h / 20) = 0.025 (m)
Calculation of the first-order eccentricity
For the mid-height section, we have:
ee  0.6e2  0.4e1 = 0.345 (m) > emin
e1 = 85.5 / 765 = 0.111 (m)
e2 = 382.5 / 765 = 0.500 (m)
Calculation of the second-order eccentricity ea
  100
- approximated method will be used
ea  (1  0.12 )( y   )
h  20ee l 02
= 0.203 (m)
h  10ee 50ic
l 0 = 10.40 (m)
ic = 0.144 (m)
2

d  d '

4is
2
= 1.421
d  d ' = 0.4 (m)
i s = 0.168 (m)
NOTE: The moment of inertia of steel is calculated according to the scheme:
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Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish Codes
I s   As i  z i
i

= 0.004
(since
N cp / N tot  70% )
N cp / N tot  1.35  400 / 765 = 70.6 %
y 
f yd
Es
= 0.00217
Calculation of total eccentricity etot
etot  ee  ea = 0.345 + 0.203 = 0.548 (m)
The total moment My :
M y  N  etot  418.91 (kNm)
Z DIRECTION
Slenderness analysis
Geometrical Slenderness

l0
= 103.92
i
The slenderness limit:
lim  35
  lim
- the column is slender for Y direction
Calculation of minimal eccentricity – 12.2.3
emin  max( 0.02; h / 20) = 0.025 (m)
Calculation of the first-order eccentricity
For the mid-height section, we have the moments defined directly, thus
ee  M / N = 127.5 / 765 = 0.167 (m) > emin
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Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish Codes
Calculation of the second-order eccentricity ea
  100
- general method will be used
etot  ee  ea  = 0.444 (m)
1
= 0.241 (m)
ea  0.1l 02
rtot
l0  12.0 (m)
1
1 1
= 0.01677
 
rtot r r f
2 y
1
1  
= 0.01306

r d  d ' 1    2  0.3
f yd
y 
Es
= 0.00217
d  d ' = 0.3 (m)
  4
ee (d  d ' )  0,1l 02 y
(d  d ' ) 2
2

d  d '

4is
= 5.135
= 1.421
2
i s = 0.168 (m)
NOTE: The moment of inertia of steel is calculated according
to the scheme:
I s   As i  y i
i

Nd
= 0.191
Ac f cd
8 g ee
1

= 0.00371
r f (1  1.4 g ) l 02
  2.0
g 
N sg l 02
10 Ec I c
= 0.156
I c = 266667 (cm4)
E c = 26411 (MPa)
  1  0,2
 10 6
1
 y ic
r
= 1.0867
ic = 0.115 (m)
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Autodesk Robot Structural Analysis Professional - Verification Manual for Spanish Codes
The total moment Mz :
M z  N  etot  339.29 (kNm)
7.3. FINAL RESULT
M y = 418.91 (kNm)
M z = 339.29 (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] Instrucción de Hormigón Estructural „EHE‟. Comisión Permanente de Hormigón. 5ª edición. Madrid,
Ministerio de Fomento, 1999.
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