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March 2014

Autodesk Robot Structural Analysis Professional - Verification Manual for Italian Codes

March 2014 page i

INTRODUCTION .............................................................................................................................................................................. 1

CCOONNCCRREETTEE ..................................................................................................................................................................................... 2

1. DM 9/1/96 – RC COLUMNS......................................................................................................................................................... 3

VERIFICATION EXAMPLE 1 - COLUMN SUBJECTED TO AXIAL LOAD AND BIAXIAL BENDING .............................................................. 4 LITERATURE ............................................................................................................................................................................. 10


March 2014 page 1 / 10

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.



CCOONNCCRREETTEE



1. DM 9/1/96 – RC columns



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 : R20 Rck = 24.10 (MPa) Longitudinal reinforcement : FeB44k fyk = 430.00 (MPa) Transversal reinforcement : FeB32k fyk = 315.00 (MPa)

3. BUCKLING MODEL

As can be seen the sway column is assumed for Z direction, and the non-sway column for Y direction.



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)).



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:

Case

N

(kN)

MyA

(kN*m)

MyB

(kN*m)

MyC

(kN*m)

MzA

(kN*m)

MzB

(kN*m)

MzC

(kN*m)

1 DL1 400 150 30 102 20 30 50*

2 LL1 150 120 30 84 10 20 40*

Dimensioning

combination 1.4DL1+1.0LL1 710 330 72 226.8 38 62 110

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)



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 maxNNd (according to point 4.2.1.2.a)

68.386325.1

max AfAf

N ydccd

(kN)

max3864710 NNd - OK

Y DIRECTION

Slenderness analysis:

i

l0 = 46.19

Check if * according to 4.2.4.2.

AcNd /

15160*

= 43.65

c

s

A

A = 1.68 %

cA = 0.24 m2

Since * the column is found as slender for Y direction. The abovementioned slenderness means that the total eccentricity of the axial force in Z

( NMc yz / ) direction will be:

atot ccc '

NOTE: If the column is found as non-slender ( * ), the total eccentricity would be atot ccc ' .

Check if the method of slenderness analysis is applicable ( *3 )

*395.13019.46 - OK

Calculation of initial eccentricity c’

For the mid-height section, we have:

21 6.04.0' ccc = 0.319 (m) > 24.0 c = 0.186 (m)

Calculation of additional eccentricity ca

300;2max 0

lcmca = 0.027 (m),

0l = 8.0 (m)



Calculation of second-order eccentricity

r

l 1

10

2

0 = 0.055 (m)

0

11

rKK

rr = 0.00861

s

yd

Ed

f

r

45.0

1

0

= 0.0075

d = 0.554 (m)

Es = 200 (GPa)

ydf = 374 (MPa)

)1;1max( effK - if creep coefficient >2 and 75 and hc '

tot

long

effN

N

150200

35.0

ckf

K 1 - in other cases

Thus, we have K 1

balud

dudr

NN

NNK

= 1.181

AfAfN ydccdud = 4503.59 (kN)

ccdbal AfN 4.0 = 1200.00 (kN)

The total eccentricity in Z direction:

atot ccc ' = 0.401 (m)

The total moment My :

toty eNM 285 (kNm)

Z DIRECTION

Slenderness analysis:

i

l0 = 45.03

Check if * according to 4.2.4.2.

AcNd /

15160*

= 43.65



c

s

A

A = 1.68 %

cA = 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

( NMc zy / ) direction will be:

atot ccc '

NOTE: If the column is found as non-slender ( * ), the total eccentricity would be atot ccc ' .

Check if the method of slenderness analysis is applicable ( *3 )

*395.13003.45 - OK

Calculation of initial eccentricity c’

For the mid-height section, we have:

dz NCMc /)(' = 0.155 (m) (the moment in mid-height section is given directly by the user)

Calculation of additional eccentricity ca

300;2max 0

lcmca = 0.020 (m),

0l = 5.2 (m)

Calculation of second-order eccentricity

r

l 1

10

2

0 = 0.036 (m)

0

11

rKK

rr = 0.01348

s

yd

Ed

f

r

45.0

1

0

= 0.0117

d = 0.354 (m)

Es = 200 (GPa)

ydf = 374 (MPa)

)1;1max( effK - if creep coefficient >2 and 75 and hc '

tot

long

effN

N


March 2014 page 10 / 10

150200

35.0

ckf

K 1 - in other cases

Thus, we have K 1

balud

dudr

NN

NNK

= 1.1483

AfAfN ydccdud = 4503.59 (kN)

ccdbal AfN 4.0 = 1200.00 (kN)

The total eccentricity in Z direction:

atot ccc ' = 0.211 (m)

The total moment My :

totz eNM 150 (kNm)

7.3. FINAL RESULT

yM = 285 (kNm)

zM = 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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