Design of Plates and
Shells
Version 11.61
This manual is protected by copyright laws. No part of it may be translated, copied or reproduced, in any form or by any means, without written permission from SOFiSTiK AG. SOFiSTiK reserves the right to modify or to release new editions of this manual. The manual and the program have been thoroughly checked for errors. However, SOFiSTiK does not claim that either one is completely error free. Errors and omissions are corrected as soon as they are detected.
The user of the program is solely responsible for the applications. We strongly encourage the user to test the correctness of all calculations at least by random sampling.
1 Task Description. . . 1−1 2 Theoretical Principles . . . 2−1 2.1. Bending Design of Reinforced Concrete. . . 2−1 2.1.1. General Comments . . . 2−1 2.1.2. Reinforcement Meshes . . . 2−1 2.1.3. Disks . . . 2−2 2.1.4. Plates . . . 2−4 2.1.5. Shells . . . 2−5 2.1.6. Other Design Codes . . . 2−8 2.2. Service Load Checks. . . 2−10 2.2.1. Minimum Thickness Check of the Compression Zone . . . 2−10 2.2.2. Crack Width Control without Direct Calculation . . . 2−10 2.2.3. Crack Width Control with Direct Calculation . . . 2−11 2.3. Shear Checks. . . 2−13 2.4. Punching Checks. . . 2−18 2.4.1. General Informations . . . 2−18 2.4.2. Column Input and Control Parameters . . . 2−21 2.4.3. Inner, Edge and Corner Columns . . . 2−22 2.4.4. Shear and Bending Design at the Column . . . 2−22 2.4.5. Special Features at Wall Ends and Wall Corners. . . 2−23 2.4.6. Punching Check Foundation Plates . . . 2−26 2.4.7. Punching Check at a Three−Dimensional System . . . 2−27 2.5. Stress Determination. . . 2−29 3 Input Description. . . 3−1 3.1. Input Language . . . 3−1 3.2. Input Records . . . 3−1 3.3. CTRL − Control of the Design . . . 3−3 3.4. CRAC − Control of the Service Load Checks . . . 3−12 3.5. MREI − Minimum Reinforcement . . . 3−15 3.6. NSTR − SLS Checks . . . 3−17 3.7. MAT − Input of Material Properties . . . 3−21 3.8. GEOM − Input of the Cross Section . . . 3−26 3.9. GEO − Input of the Cross Section in cm . . . 3−28 3.10. DIRE − Definition of Orthogonal Two−course Reinforcement 3−29 3.11. THRE − Definition of Skew 2− and 3−course Reinforcement 3−32 3.12. PARA − Design Parameter . . . 3−34 3.13. PUNC − Punching Design . . . 3−37 3.14. LC − Selection of Design Load Cases . . . 3−40
ii
3.15. GRP − Selection of Groups . . . 3−42 3.16. ELEM − Selection of Elements . . . 3−44 3.17. NODE − Selection of Nodes . . . 3−46 3.18. S − Input of External Forces and Moments . . . 3−48 3.19. ECHO − Control of Output . . . 3−49 4 Output Description. . . 4−1 4.1. Design Parameter . . . 4−1 4.2. Design Results . . . 4−4 4.3. Reinforcement List . . . 4−6 4.4. Design Moments or Membrane Forces . . . 4−6 4.5. External Defined Forces and Moments . . . 4−7 4.6. Punching Check . . . 4−8 4.7. Fatigue and Stress Amplitude Check . . . 4−9 4.8. Stress Determination . . . 4−10 4.9. Reinforcement Indexel Index . . . 4−11 5 Examples . . . 5−1 5.1. Bending Design. . . 5−1 5.2. Design with Service Load Checks. . . 5−8 5.3. Building Construction Plate. . . 5−14 5.4. Building Construction Plate with Balcony. . . 5−21 5.5. Design with DIRE and THRE for External Forces. . . 5−32 5.6. Examples in the Internet. . . 5−35
1
Task Description
.
The internal forces and moments which have been calculated with the pro-grams SEPP, TALPA or ASE or superimposed with the program MAXIMA are stored in the database or they are input as so−called external forces and moments. The program BEMESS is used for the reinforcement design ac-cording to DIN1045−1988, DIN 1045−1, OeNORM B 4700, Part 8 and 9, Euro-Code 2, Part 1, British Standard or ACI_318M, or it determines the extreme stresses according to the linear elastic theory.
When the design is performed for several load cases, the result of the design calculation represents the maximum reinforcement amount which is calcu-lated from these load cases. BEMESS does not perform any load case super-positions. This is the task of the program MAXIMA.
Additionally to the calculation of the statically required reinforcement, the program may perform the so−called working load checks. These include the crack width control and the crack reduction check. They are complemented by the check of minimum thickness of compressive zones which is frequently required in civil engineering.
The compression reinforcement for shells and disks is calculated equivalently to the tensile reinforcement according to the stress state. For this the require-ments of the minimum reinforcement of the respective code are taken into consideration (e.g. minimum compression reinforcement of the statically re-quired cross section, minimum reinforcement of diaphragm girders). The ap-propriate parameters are preset according to each code. Notice that the de-finition of these parameters with zero makes this control ineffective. The use of compression reinforcement in plates is not a part of a good engineering practice. Therefore a warning is issued in the case of compression reinforce-ment in designed cross section.
A centre point or an axis in the middle can be defined for circular plates, cylin-ders or similar structures. A tangential and a radial reinforcement are calcu-lated then for all included elements or nodes (so−called circular reinforce-ment).
The program performs a punching check at point supports (columns) as well as at wall corners and wall ends, if the necessary load cases of the maximum support reactions are available.
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2
Theoretical Principles
2.1.
Bending Design of Reinforced Concrete
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The reinforcement design is based on the method described by Baumann (Der Bauingenieur 47 (1972), pages 367−377). Three design cases are distinguished: Disks, plates and shells.
2.1.1.
General Comments
The design strategy pursued by the program BEMESS is independent of the real available internal forces and moments. It depends only on that with which programs the results were made and/or which mechanical model was declared in the case of the external forces (see CTRL SYST). So for example a system, which was defined as a shell, is also calculated as a shell, even if it only contains plate or disk loading.
The position of the three−course and/or skew two−course reinforcement mesh (record THRE) must be defined clearly by the user. In the case of an orthogonal (two−course) reinforcement mesh (record DIRE) the choice of the position can be left also to the program. The principal reinforcement is inserted then either in the direction of the x axis or in the direction the y axis. For circular plates a radial and a tangential orthogonal reinforcement can be determined through the input of a centre point.
The previous programs SEPP (plates), TALPA (disks) and ASE (shells) determine the internal forces and moments in the local coordinate systems of the plane finite elements (see appropriate manuals). In BEMESS both the directions of the reinforcement layers and the terms ’upper’ and ’lower’ are oriented at the local coordinate systems; ’lower’ is at the side of positive z axis. Particularly in the program ASE the user should realize the characteristics of the local coordinate axis definition. For the programs SEPP and TALPA the local and global coordinate systems are identical.
2.1.2.
Reinforcement Meshes
In most stress situations the orthogonal two−course reinforcement mesh is the optimum solution of the design task.
Skew two−course reinforcement meshes are chosen mostly due to constructive considerations. They are static generally less effective than
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orthogonal nets. The steel requirement increases more than linearly with the skewness of the reinforcement mesh. A two−course reinforcement is only al-lowed for 90 up to 60 degree skewness. For higher skewness a third layer is necessary to avoid large crack width.
Three−course reinforcement meshes are the best statical solution for the case of an elliptic stress state (universal tension or compression): The required steel amount is minimal, i.e. it corresponds to the required cross section of an orthogonal reinforcement mesh laid parallel to the principal stresses. On the other hand there is no three−course solution for the case of the hyperbolic stress states (simultaneous tension and compression). For this a radically minimised two−course solution is sought. This is done via breaking off of this reinforcement layer which is used least statically. The stiffening compressive concrete force which generally must be assigned to another direction, however, is set at this place.
The loading of the heterogeneous reinforced concrete continuum is transformed according to the compliance of the internal force equilibrium along the reinforcement directions (tension or compression) and the stiffening fictitious compression strut of the concrete. The concrete stress can be checked only when the reinforcement layers get their statically required cross section due to the design. If the permissible compressive concrete stress is exceeded, a compression reinforcement is inserted if possible.
2.1.3.
Disks
The stresses σx, σy and τxy are transformed into the selected or by the program calculated reinforcement direction. Reinforcement is considered for the tensile stresses. It is checked whether the material can include the compressive concrete stresses. The suggested reinforcement takes into consideration the requirements of the implemented codes with regard to the minimum reinforcement of diaphragm girders and allows the use of equal reinforcements amounts at both sides of the disk. The reinforcement design is only reasonable and permissible for structural parts analysed in a plane stress state!
Safety factors design:
For all tensile reinforcements the literal SS1 (for usage of DIN1045−1988 SS1=1.75) is used (see record MAT). SC2 and SS2 are used for the determination of the permissible concrete compressive stress as well as for compression reinforcement (for usage of DIN1045−1988 SC2=SS2=2.1).
Steel stress compression reinforcement:
A maximum steel stress of 400 N/mm2 (2 promille strain at E=200000 N/mm2) divided by SS2 is used for DIN 1045−1, EC2 and Ö−Norm B 4700 (for DIN1045−1988 420 N/mm2 due to E= 210000 N/mm2).
Permissable concrete compressive stress:
In accordance to the recommendation by Schlaich/Schafer (In: Konstruieren im Stahlbetonbau, B.K. 1993/II, S.378), the permissible compressive concrete stress is reduced to 80% (DIN 1045−1 + Fachbericht 75%) of the effective compressive concrete strength βR, if lateral tensile stresses are available. For lateral compression 100% are approved. In the region of 0.0 to 0.1 N/mm2 the tensile stress (with reference to the bare concrete cross section) is reduced linearly from 100 % to 80 % (or 75%). The con-crete stress is checked and compression reinforcement added if necessary − the lever arm will not be adapted! This reduction can be switched off with CTRL TENS 0.
Compression reinforcement:
If the principal compressive force can not be included by the concrete alone, a compression reinforcement must be inserted additionally. This, however, is not always possible for all the cases due to the equilibrium considerations. As an example a column that is loaded uniaxially with βR is mentioned. If only a reinforcement mesh is allowed now smaller than 45 degrees, then also a high reinforcement can not hold the uniaxial principal compressive force, since the reinforcement mesh is predeformed to a lozenge because of missing lateral compression and it is not able to withstand the force.
If the reinforcement is inserted with a smaller angle, for example an angle with a 10 degree deviation to the principal compressive force, then this reinforcement direction can take up a compressive force. The transverse reinforcement gets then a tensile force which can be interpreted as a splitting force. For the equilibrium of the external loads nx, ny, nxy with the inner forces of the concrete compressive force and the forces in the reinforcement directions it is now necessary, that the concrete compressive force is set a little bit skew (from the compression reinforcement away).
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Now the concrete compressive force is not in line with the external principal normal force. If the angle reaches 45 degrees between the new concrete compressive force and the principal compression reinforcement, then no further loads can be taken up anymore. Now it is not possible to design the cross section. Then the error message ’Angle between compressive force and compression reinforcement too large’ is printed.
CTRL PFAI 2 can be used to alleviate this mechanically exact procedure and therefore to avoid the error message. The non absorbable concrete compressive force is then fully taken up by the reinforcement and it is assumed, that the compressive force of this inserted compression reinforcement is transferred to the neighbouring elements. Usually this is possible at singular points and at re−entrant corners, but not possible at free edges!
For special cases the design for the relevant elements can be repeated in a 2nd calculation with a three−course reinforcement (one additional 45−degree−reinforcement bar).
If the reinforcement is exactly in the principal compressive force direction, any arbitrary compressive force can be added then about the reinforcement increase until the maximum permissable 9% of the reinforcement content is reached.
Minimum reinforcement of the pressed cross sections for disks:
The cross sections designed with BEMESS are always considered as "reinforced walls". Even if no reinforcement is necessary for certain statical points, the points are still considered as a part of a reinforced wall. A classification according to DIN1045−1988 chapter 25.5.5.2(2) does not occur. A minimum reinforcement with 0.8% (= default in record MAT ... AM3) of the statically necessary cross section is always inserted. The minimum reinforcement calculation occurs in the direction of the principal stresses. The skew reinforcement is considered with the square of the cosine of the angular deviation.
2.1.4.
Plates
The plate moments m−x, m−y and m−xy are transformed according to the method of Baumann into two or three design moments along the specified
reinforcement directions. For this case the lever arm of the inner forces is determined in dependence on the compression zone utilization. The design of the necessary reinforcement cross sections occurs according to the material strengths and laws of the respective code.
The increase of the effective moments according to DIN1045−1988, chapter 17.2.1(6) in the case of the small statical efficient heights are taken into consideration.
Safety coefficients design:
For all calculations the literals SS1 and SC1 (for usage of DIN1045−1988 SC1=SS1=1.75) are considered for the high compression zone utilization, because for a possible case of the steel extension less than 3 per mille a compression reinforcement is arranged (see Betonkalender 1994 I S. 385).
Steel stress compression reinforcement: is not limited for plates Permissible concrete compressive stress −−> see disks
Compression reinforcement plates
For plates a compression reinforcement is only allowed, if the reinforcement directions agree at the upper and lower plate side, because only then it is guaranteed, that the stiffening force of the reinforcement mesh can be considered by the opposite tensile side. No compression reinforcement is approved for plates with twisted reinforcement directions of the upper and lower side.
For lateral tension the necessary reinforcement is higher than for lateral compression, because the compressive force taken up by the concrete is smaller due to a lower permissible concrete commpression stress. In this case the lever arm also becomes smaller and the smaller permissible concrete compressive stress is reached faster. This means that compression reinforcement is inserted earlier. The reduction of the permissable concrete compressive stress for lateral tension can be eliminated with
CTRL TENS 0.
Minimum reinforcement of pressed cross sections is not valid for plates.
2.1.5.
Shells
The moments m−xx, m−yy and m−xy as well as the membrane forces n−xx, n−yy and n−xy are converted to effective membrane forces acting on fictitious
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disks with a thickness of 0.35⋅construction element thickness at the outer shell side. The loading consists of force pairs divided up into bending moments and halved membrane forces. The lever arm of the internal forces required for the decomposition of the bending moments is not assumed according to BAUMANN. It is calculated at the basis of full utilisation of the compressive zone. For this the lever arm is determined for two characteristic directions (the principal bending moment direction and the principal normal force direction). The smaller lever arm is used then for the segmentation of the moment into membrane forces. The average concrete cover between the principal and lateral directions is applied as concrete cover.
Fictitious disks and lever arm for shells (DIN1045−1988) Please notice the different symbols:
DIN1045−1988 DIN 1045−1, EC2, BS, ACI, EHE and OeNORM B 4700
d=element thickness d = efficient reinforcement height h=effective depth h = element thickness
For approximately centrically pressed shells the cross section could not be used completely due to the limit of the equivalent thickness of 0.35⋅h. Therefore in this case the equivalent thickness is increased for centrically pressed shells up to the value 0.5⋅thickness⋅SC1/SC2. The 0.35⋅thickness is applied from an eccentricity e/d >0.20. For a smaller eccentricity it will be interpolated.
The mesh reinforcement design occurs separately for the two fictitious disks at the shell outer sides. The shear design is performed similarly to that of plates.
Safety coefficients design:
Also for strongly pressed cross sections with small moments SS1 is employed always for the reinforcement at the tensile side (for usage of DIN1045−1988 SS1=1.75), because through the zone thought in the interior without compressive stresses (0.30⋅construction element thickness) a reduction of the tensile steel strain less than 3 % is not possible.
If tensile reinforcement is necessary, the compression reinforcement might be calculated then too with the safety of 1.75. Since the compressive force direction in the compressive zone in general deviates from the tensile force direction in the tensile zone for shells, however, the compression reinforcement is designed always with SS2 (for usage of DIN1045−1988 2.1), because in the compressive force direction in the compressive zone the cross section can be overpressed completely.
For the determination of the permissible concrete compressive stress SC1 (1.75) is considered always for shells in contrast to disks, because only 2⋅0.35⋅construction element thickness and/or 0.5⋅thickness⋅SC1/SC2 is used for centrical compression.
Permissible concrete compressive stress −−> see disks Permissible steel stress −−> see disks
Compression reinforcement:
To the absorption of the compressive force in the thought disk at the shell outer side only their thickness of 0.35⋅construction element thickness is available. In the intervening area no compressive stresses can be excavated. A compression reinforcement in the thought disk is allowed then like for −−> disks with consideration of the lateral compression. In problematic cases the reduction through the lateral compression can be disconnected with CTRL TENS 0.
Minimum reinforcement of pressed cross sections
Cross sections designed with BEMESS are considered always as "reinforced walls". A classification according to DIN1045−1988, chapter 25.5.5.2(2) does not occur. The minimum reinforcement
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calculation occurs in direction of the principal stresses. Reinforcements which lie skewly to this are considered with the square of the cosine of the angular deviation.
In contrast to the bending design the minimum reinforcement for shells can be calculated not independently in two separate disks, but it must be considered at the total cross section (0.8 % of the necessary total cross section). Therefore the total construction element thickness is used for axial compression in this case with a safety factor of SC2 (2.1).
For normal force with bending at least 0.5⋅AM3 (0.4%) are considered at the tensile side" (DIN1045−1988, chapter 25.2.2.1).
2.1.6.
Other Design Codes
Special features of the Eurocode EC 2 1992−1−1:2004 (E) und :2005 (D) Following boxed values according to NA 005 07.01.00 N 0196 are used:
− # 12 − 3.1.6(1)P α−cc (fcd=α−cc*fck/γc) − # 15 − 3.2.7(2) Design ultimate strain
The original version 1992−1−1:2004(E), aktivated with country code 0, uses concrete with much higher strength (alpha−cc = 1.0). Steel is limi-ted at a high design ultimate strain of 0.9*50 o/oo (−> max σ=545 N/mm2).
Special features of the Russian SNIP 2.03.01
The concrete strength FC (Rb) and FCTK (Rbt) (see program AQUA
re-cord CONC) are reduced with an additional building factor γb2. It can be set with CTRL SNIP and is preset to 0.9. Steel is only used bilinear up to FY, for shear FP is used for Rsw.
Special features of the Swedish BBK 04 and BBK 94
Important is here the additional safety coefficient gamma−n in depen-dence on the safety class (1,2 or 3). The safety class is defined in pro-gram AQUA via record NORM at CAT:
NORM S BBK−04 or BBK−94 CAT 1: gamma−n=1.00 CAT 2: gamma−n=1.10 CAT 3: gamma−n=1.20
To change the safety class, an AQUA run with only an input for record NORM can be set in front of the BEMESS.
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2.2.
Service Load Checks
.
If requested with the input, the following checks are performed after each other. If necessary the reinforcement is increased which is requested statically by the appropriate amount.
2.2.1.
Minimum Thickness Check of the Compression
Zone
The program calculates the compression zone height in the principal moment direction and in the principal axial force direction. The smaller value is decisive. The design is performed according to the formulas in Betonkalender 1992/I, pages 465−466. For this purpose the reinforcement whose the direction does not usually coincide with the direction of the checked section normal gets converted in the checked direction.
If this check is concluded without a reinforcement increase, it is followed with the check 2.2.4, if requested. If it turns out that the required minimum thickness of the compression zone is not kept with the statically required reinforcement, the check 2.2.4 may occur at first, so that the possible reinforcement increase which results from it may be taken into account in handling the present check. The compression zone thickness is adjusted then to the required value through iterative variation of the reinforcement. The standard check is performed separately in the two principal moment directions. A stricter check can be requested with CTRL THIC FULL (see record CTRL).
The check is requested with an input XMIN in the record CRAC.
2.2.2.
Crack Width Control without Direct Calculation
The check limits the available steel stress during usage to the permissible value according to the tables of the corresponding standard:
DIN1045−1988: Table 14
DIN 1045−1: Table 20
EC2: Table 4.11
OeNorm B 4700: Table 9 und 10
EHE(2000): Input via SIGO, SIGU in record GRP
For the crack design according to DIN 1045−1 table 20 other crack widths are possible. The table values are determined according to Heft 525 page 196
equation (21). For crack check according to DIN 1045−1 the interpretations of the Normenausschuss Bau NABAU (No. 123) are considered.
It is assumed a crack formation through load. A crack internal force for example according to DIN1045−1988, chapter 17.6.2(3) is not considered. For thick plates the limit diameters are increased according to the standard. According to OeNORM B 4700 table 9+10 ht=0.5⋅h is always used also for shells with normal forces because of the problematic nature of different tensile zone heights in different directions! Only for disks h=t is used there. For arbitrary crack widths the interpolation of the maximum bar diameter is done according to table 9 and 10 OeNORM B 4700.
For the Eurocode EC 2 1992−1−1:2004(E) and :2005(D) following boxed value is used according to NA 005 07.01.00 N 0196:
− # 68 − 7.3.4(3) Analysis of the crack width
For the limitation of the crack width a tabular check according to EN 1992−1−1:200.. 7.3.3 (CRAC WK TAB) is implemented. The calculation of the crack width is done according to EN 1992−1−1:200.. 7.3.4 (CRAC WK 0.15) and the minimum reinforcement according to EN 1992−1−1:200.. 7.3.2 (MREI...).
Minimum reinforcement für early restraint according to DIN 1045−1:
According to NABAU No. 238 from November 2005 to 11.02.2 Tab. 20 the table 20 is extended for steel stresses lower than 160 N/mm2.
For the Swiss code SIA 262, the Russian code SNIP 2.03.01 and the Swedish code BBK 04 and BBK 94 the crack width check is done with CRAC WK TAB and the check for the steel stresses with GRP...SIGU (or PARA SSU). For these codes a direct crack width design according to EC2 4.4.2.4 is alternative possible with CRAC WK 0.15.
The check is requested with the input DDES in the record CRAC as well as an input of the environmental conditions or the crack width in the record ELEM or NODE. CRAC...WK must not be input for this check according to the tables! It is implemented for all reinforcement types DIRE and THRE.
2.2.3.
Crack Width Control with Direct Calculation
If the simple check according to the tables is not sufficing, a direct calculation can occur with the default of the permissible crack width:
DIN1045−1988: Calculation according to Schießl Heft 400 DAfStB
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DIN 1045−1: Calculation according to the equation of the standard DIN 1045−1
EC2: Calculation according to EuroCode 2
article 4.4.2.4
The method should be used only in special cases. In the normal case the limitation of the crack width without direct calculation according to the tables is recommended.
The precise" check is requested with an input WK and DDES in the record
2.3.
Shear Checks
.
A shear check is performed for plates and shells. The critical shear force V is determined from the shear forces VX and VY via a geometrical addition. This shear force, divided by the lever arm of the internal forces (see bending design), results in the effective shear stress τ0.
Three cases are distinguished according to DIN1045−1988: • τ0 < τ011:
no shear reinforcement necessary (shear zone 1); • τ0 < τ02:
Shear reinforcement is required (shear zone 2). The necessary shear reinforcement is τ/βs; τ is either equal to τ0 in the case of the permanent loads which are not mainly stationary or it is equal to the reduced shear stress value according to DIN1045−1988, equation 17, in the case of the permanent loads which are mainly stationary;
• τ0 > τ02:
without input τ03: inadmissible stress region (shear zone 3) with input τ03: shear zone 3 until τ0 = τ03
with full shear consideration (girder constuction elements)
The output includes the shear zone, the existing shear stress τ0 and possibly the shear stress τ which has to be considered. Perpendicular links are assumed during the calculation of the required shear reinforcement. The shear reinforcement can be output in reference to an area (cm2/m2) or to the elements (cm2).
The shear design according to DIN 1045−1, EuroCode 2 and OENORM B 4700 is based on three design values of the sustainable shear force:
• VRd1:
Design value of the sustainable shear force without shear reinforcement
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Maximum design value of the sustainable shear force with shear reinforcement, which can be sustained without failure of the fictitious compression concrete strut. If this value is exceeded by the existing shear stress Vsd, the cross section can not be designed (corresponds to shear zone 3 according to DIN1045−1988).
• VRd3:
Design value of the sustainable shear force in a cross section with shear reinforcement (assigned to the shear zone 2). The amount of the required shear reinforcement depends on this value.
For shear design according to DIN 1045−1 the minimum shear reinforcement is complemented corresponding to the interpretations of the Normenaus-schuss Bau NABAU (No. 131): ’For plates b/h>5 a minimum shear reinforce-ment has to be considered with 0.6ρ according to table 29 in case of VED>VRd,ct.’
In BEMESS the method with variable compression strut inclination is implemented. The compression strut inclination is determined in this case according to the utilization degree.
As VRd1 depends on the longitudinal reinforcement, for first V>VRd1 there are two possibilities − either compute shear reinforcement or increase longitudi-nal reinforcement to increase VRd1. This can be controlled with CTRL ro_v
for the overall slab or with PUNC ro_v for punching regions. Example of an input in BEMESS6.dat:
CTRL RO_V 0.5 $ The program attempts not to use any shear reinforcement
$ up to this bending reinforcement ratio. The shear check
$ increases perhaps the bending reinforcement up to this value.
PUNC D 0.30 B 0.30 ro_v 1.50 $ default single column dimensions
For EC2 the standard method is checked and used additionally, if it delivers a smaller shear reinforcement. Therefore also a minimum shear reinforcement is used for V>VRd1 with 60% of the values of the table 5.5 according to EC2 (Betonkalender 1998−I−S.242).
During the calculation of VRd1, VRd2 and the compression strut inclination the available longitudinal tensile and longitudinal compressive reinforcement as well as the normal force to be included in the principal shear force direction are considered. Reinforcements are considered in this case with the square of the cosine of the angular deviation to the principal shear force direction.
The basic value of the shear strength according to EC2 and OENORM is to be input in the record MAT at item TRD, if defaulted values are not used. For DIN 1045−1 no shear stress limits may be input. The design occurs there exclusively due to the concrete stiffness f−cd.
Reinforcement in steps is input at record MAT item K.
The shear design according to British Standard occurs like the check according to EC2. The from the concrete alone sustainable shear stress v−c is determined in this case in dependence on the bending reinforcement in principal shear force direction according British Standard Table 3.9.
The shear design of the American standard ACI occurs according to ACI_318M_11.3 "Strength design" with the differentiated concrete design resistance Vc according to bending, compressive or tensile bending. In general a material safety of 0.85 (ACI_318M_B.9.3.2) is used for the shear.
Special features of the Eurocode EC 2 1992−1−1:2004 (E) und :2005 (D) Following boxed values according to NA 005 07.01.00 N 0196 are used:
− # 45 − 6.2.2(1) Shear VRd,ct analysis
− # 47 − 6.2.3(2) max. compression angle cot0 Special characteristics D not equal to E:
For shear in D and E, VRd,ct and VRd,max are calculated with different factors. The additional limitation of the compression strut inclination according to DIN 1045−1 equation (73) is not known in the original EC2.
Special features OENORM B 4700 − difference to EC2
Unlike the original EC2 the standard method in the shear design which shows a smaller shear reinforcement at weak loaded cross sections may not be employed here. The compression strut inclination beta is limited to 0.6 (according to B4700 equation 23).
Special features French Design Code BAEL 91 Revision 99 − difference to EC2
Shear design ass = γs⋅ (τ−u−0.3ftj⋅ k)/(0.9fe)
max. shear stress 0.2fcj/γb or 5 MPa (compression strut)
Special features Italian Design Code D.M.9 genniao 1996 − difference to EC2
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Plates without shear design are allowed to
VSduv 0.25 @ ffcd@ r @
ǒ
1.0) 50 @ òǓ
@ bw@ d @ d otherwise shear design with VSdu ≤ Vcd + Vwdwith Vcd = 0.60fctd ⋅ bw⋅ d ⋅ δ max. shear force 0.3fcd⋅ bw ⋅ d
minimum shear reinforcement min−Vwd = 0.5 ⋅ Vsdu Special features Swiss Code SIA 262
In shear design, BEMESS tries to avoid shear reinforcement by in-creasing the longitudinal reinforcement up to RO_V to increase the member resistance MRd (see CTRL RO_V). If shear reinforcement is necessary, with SIA 4.3.3.4.5 an optimum compression angle is calcu-lated. The value kc is set to 0.6.
Special features of the Russian SNIP 2.03.01
For the concrete steel the value FP is used for Rsw (see program AQUA record STEE). In shear design, BEMESS checks the compression strength according to SNIP equation (72). Shear reinforcement is necessary, if the shear stress reaches the concrete part Qb according to SNIP (76). Then links will be computed for Q−Qb with the assumption
of 45 degree compression angle. Minimum shear links will be taken into account according to SNIP equation (82).
Special features of the Swedish BBK 04 and BBK 94
The shear check is done according to the alternative model which is de-scribed in BBK 04−3.7.3.7. This model corresponds except for some fac-tors DIN 1045−1. As for DIN−Fachbericht a minimum value vmin is used for the concrete bearing capacity. For the shear check the program attempts to increase the member resistance VRdc via an increase of the longitudinal reinforcement up to RO_V (see CTRL RO_V) in order to refuse a shear reinforcement. If a shear reinforcement is necessary, an optimal inclination compression strut is determined according to 3.7.4.3d. However, this compression strut inclination becomes not smaller than cot−teta≤1.5 due to BBK 04−figur 3.7.4.3b. If shear links necessary, they are designed to fsv=fst according to 3.7.4.3f. A minimum shear reinforcement is not checked.
The shear check for BBK 94 is done according to the old model. Slight normal forces taken here into account for the concrete part Vc with 0.1⋅Nd according to 3.7.3.5.
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2.4.
Punching Checks
.
2.4.1.
General Informations
Precondition
Load cases with support reactions have to be contained in the indicated load cases. If the internal forces and moments from the program MAXIMA are designed, the program BEMESS has to be informed also about the load case of the extreme support reactions (record LC).
The use of boundary elements for linear wall support is the precondition for the automatic identification of wall ends and wall corners. An elastic edge support is recommended. The stiffness of this linear edge support results to c=E⋅D/h (with h=wall height) in this case and can be input generally with approximate 500000 kN/m for the usual building constructions. Indeed a PZ support with an additional output edge element is possible, however, high singular corner moments which depend on the element mesh strongly are calculated then at the re−entrant corners!
Processing
The program searches then single support nodes (single columns) and wall ends as well as wall corners and performs a punching check for these points. Nodes with less than 5 kN support reaction are not considered! This has to be considered for the control of the punching points (with program WING QUAD ASPS SCHH 0.20")!
Within the punching area (see figure) the plate shear design is replaced then by a punching check. The elements lying within this area get then at least the for the punching check necessary upper longitudinal reinforcement. If the bending design shows a higher longitudinal reinforcement, this becomes determinent. A normal plate shear design occurs outside of the punching area.
A consideration of studrails is not planned currently (see Column Input and Control Parameters). The program can be informed (PUNC ... HEAD=DUEB), however, that the check is supposed to be performed later. No increase of the upper longitudinal reinforcement occurs then. The program does not interrupt with a design error in spite of incorrect punching. The in WING with ***** marked columns can be checked subsequently manually.
Punching area Punching area
Determinent cut
Determinent cut and punching area according to DIN1045−1988 Please notice different symbols:
DIN1045−1988 DIN 1045−1, EC2, BS,
ACI, EHE and OeNORM B 4700 d=element thickness d=reinforcement effective depth h=effective depth h=element thickness
According to DIN 1045−1, EC2 and British Standard a determinent round cut is defined according to the standard in the distance 1.5⋅effective depth. For the input of an enlarged column head the program verifies the external punching cut (in the thinner plate). In the thicker enlarged column head no check is necessary for the sufficient thickness DHEA. For 1.5⋅(effective depth+hS) ≥ LS in this case LS is reduced to hS according to DIN1045−1988. For LS > 1.5⋅(effective depth+hS) follows a warning that the shear cut is to be performed within the stiffening by the user.
The critical round cut is to be performed for flat slabs in the case of DIN1045−1988 with a diameter of dR=dS+effective depth which corresponds to a distance of the effective depth/2 from the column. The distance is 1.5⋅effective depth for DIN 1045−1, EC2 and British Standard. A perhaps necessary punching shear reinforcement is calculated for DIN1045−1988 and EC2 in a distributed form in a ring area with a width of 1.5⋅effective depth. For DIN 1045−1 and British Standard the necessary number of round cuts (perimeter) to be reinforced and their in each case necessary reinforcement in cm2 are determined (ECHO PUNC FULL). The total reinforcement in cm2 (sum of perimeter) is printed always in the list of the punching checks.
Special features of the Eurocode EC 2 1992−1−1:2004 (E) und :2005 (D) Punching design is done with the critical perimeter at 2.0*d. An
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tional check at the column face is added. As the german version NA 005 07.01.00 N 0196 does not give boxed values, punching is then calculated acc. DIN 1045−1.
Special feartures OENORM B 4700 − difference to EC2
The original EC2 equation with 40⋅ro1 is used for VRdc for punching and not the equation (44) of B 4700, because the span l in the case of FE plates is in general unknown. VRds is limited to 1.4⋅VRdc. The punching reinforcement is approximately twice so large as with the original EC2 due to the effective coefficient ks!
Special features according to American Standard ACI
Punching occurs with marking (without precise particularization) of possible necessary shear arms according to ACI_318M_11.12 "Strength design". Like for the shear check a material safety of 0.85 (ACI_318M_B.9.3.2) is used also here.
Special features French Design Code BAEL 91 Revision 99 − difference to EC2
Punching form: rectangle around the column Check of the shear stress in distance d/2
If not possible without shear reinforcement, then a warning is printed with reference to manual determintation of punching reinforcement. Special features Italian Design Code D.M.9 genniao 1996 − difference to EC2
Punching is only checked according to EC2. If not possible without shear reinforcement, then a warning is printed with reference to man-ual determintation of punching reinforcement.
Special features Swiss Code SIA 262
Punching is checked according to german DIN 1045−1, because in SIA 262 the span length l and the resistance MRd influence are not known in general. The collaps reinforcement according to SIA 262 4.3.6.7.1 is taken into account. If necessary punching must be checked according to SIA 262 separately. The collaps securing is considered according to SIA 262 4.3.6.7.1.
Special features of the Russian SNIP 2.03.01
Punching is checked according to original EC2 and if necessary, it must be checked separately.
Special features of the Swedish BBK 04 and BBK 94
Punching is checked at a perimeter 0.5⋅d. The punching excentricity factor η is set to 1/1.15 for inner supports, 1/1.40 for boundary supports und 1/1.5 for edge supports, according to common EC2 regulations. A design with punching shear reinforcement is not allowed in BBK 04 and BBK 94. Also a check for the for column heads is not done.
So that a necessary shear reinforcement will not forget in the graphics, all points have the shear reinforcement in the punching area, also the points directly about the column!
If no column dimensions are input, BEMESS uses a rectangular column with d=b=plate thickness (however, not larger than 30 cm) as default. Column dimensions possibly defined in the data base are accepted (Slabdesigner). With ECHO PUNC FULL a detailed output is printed per column.
Examples for wall and column punching checks are to be found in the Internet at www.sofistik.com/bibliothek.htm in the statics examples.
2.4.2.
Column Input and Control Parameters
The manual input or modification of the column parameters occurs with:
PUNC TYPE X Y Z D B HEAD DHEA REIN MREI P LC_P
where the columns are assigned by means of the supporting coordinates X and Y (mesh−independent). If no input for X+Y occurs in spite of an input D,B,HEAD,DHEA,REIN or MREI, the values are used for all columns. The program attempts to perform first of all the punching check without shear reinforcement. If bending reinforcements more than REIN (default 1.5 %) results, so the program changes to punching check with shear reinforcement.
According to DIN1045−1988 0.5 % longitudinal reinforcement is used, if the shear stress is more than τ011a (is disconnectible with PUNC MREI=0.0).
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For the consideration of studrails see General Informations".
With PUNC TYPE=NO the punching check is not considered (= default for shell structures).
2.4.3.
Inner, Edge and Corner Columns
For edge and corner columns the effective round cut u is smaller than u0=PI⋅(dS+ effective depth). In addition the calculated shear stress has to be increased there around 40 % (DIN−1045−1988).
BEMESS determines itself the effective round cut automatically, when it is controlled whether in individual sectors around the column blockouts or edges are to be found. It applies in this case individual sector areas like for the block load analysis (SEPP−BBLO). If for a sector area plate elements are used with 100%, the sector is considered as effective for the punching. Currently 36 sectors are arranged with 10 degrees per sector. The search sectors extend from dS/2 to dS/2+6⋅effective depth.
All effective search sectors together produce the effective perimeter u of the punching round cut. The ratio u/u0 is output in % in the result list.
A column is considered as an inside column from 1.00⋅u0 to 0.80⋅u0., as an edge column from 0.80⋅u0 to 0.49⋅u0, as a corner column smaller 0.49⋅u0. According to the standard the shear stress in the round cut determined with u is increased with the following factor for the rough consideration of not axisymmetric bending loading:
Increasing factor of the calculated shear stress in round cut:
Standard: DIN−1045−1988 1045−1 EC2 BS ACI
Inner column 1.00 1.15 1.15 1.15 is consi− Edge column 1.40 1.40 1.40 1.40 dered at Corner column 1.40 1.50 1.50 1.40 Vc
2.4.4.
Shear and Bending Design at the Column
Within the punching area the regular plate shear design is omitted and replaced by the punching check.
The high node moment in a singular supported node is reduced with delta−m = A/8⋅bmin/bmax (A = maximum support reaction, bmin, bmax = smaller, larger column dimension). It is considered, that for biaxial moment loading (mI=mII) the support pressure can be determined only in each case to a half
for a mI and a mII support moment reduction, therefore delta−mI= A/16 and delta−mII= A/16 for bx=by. The moment reduction is limited to max. 20 %. In addition a larger thickness is used during the bending design of the central column node. In this case the thickness is increased from the column edge with 1:3. With the default of a plate thickness in the record GEOM as well as at wall ends and wall corners this increase does not occur. The increased thickness is printed in the case of ECHO REIN FULL per node.
Design thickness in the central node
2.4.5.
Special Features at Wall Ends and Wall Corners
The critical round cut is used only at the wall front edges and at the wall lateral edges according to the new DIN1045−1 picture 38. The support forces are transformed in a smeared linear reaction and then integrated over a length of a1/2 as shown in the pictures below. The single node force of the corresponding edge node is used, however, at least to 2/3. The shear stress τ−R is always increased around 40 % due to the non−axisymmetric loading. For EC2 and British Standard the values are valid according to the standard. The program uses a wall thickness D with 24 cm as an effective support wall area for the default as well as a corresponding wall length according to the design code. If a wall thickness already exists in the database, this is used so. A load increasing factor of 1.05 is considered at wall ends for a normal design. According to Betonkalender 2006−II page 186 the DIN defines no load in-creasing factor for wall ends and wall corners. In the example according to Betonkalender the load increasing factor is used however with 1.40, on the other hand a longer check cut is selected with the side length of 1.5⋅d. BE-MESS sets the side length to 1.0⋅d according to DIN and selects the load incre-sing factor with 1.05. Thus a "balanced design" described as in the Betonka-lender is reached. It is also possible to use a load increasing factor of 1.40, if an integration of the loads is defined to 1.5⋅d or smaller with CTRL WINT 1.5. Thus smaller punching loads result then, however. Another possibility is to increase the side length with CTRL WEND 0.60.
Legend 1 Load area Aload
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a1vȥ
ȡ
Ȣ
a 2b 5, 6d * b1 b1vNJ
b2, 8dDIN1045−1, figure 38 − Determinent sections for the critical round cut in the case of extensive support areas
ÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉ
1
Wall endÉÉÉÉÉ ÉÉÉÉÉ ÉÉÉÉÉ ÉÉÉÉÉ ÉÉÉÉÉ ÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ ÉÉÉÉÉÉÉÉÉÉÉ
1
Wall cornerLegend 1 Load area Aload
If two wall ends are direct side by side, u is limited to 0.6⋅u0 in order to prevent an overlap of the round cuts. The design moment is reduced. An increase of the plate thickness in the central node does not occur, however, because in the rule it is supported onto a masonry wall.
Input example:
PROG BEMESS HEAD
ECHO full no; ECHO para,punc full
PUNC WALL D 0.365 $ default wall thickness
PUNC WALL X 3.20 Y 5.26 D 0.24
PUNC WALL X 8.15 Y 2.10 HEAD DUEB
PUNC D 0.40 B 0.40 $ dimension single column
LC (801 806 1) $ MAX−MIN load cases of the extreme bending moments
LC 901,902 $ MAX−MIN load cases of the support reactions
GEOM HA 30 DHA 10 HB 30 DHB 10 $ ** concrete cover
DIRE 0 0 $ ** reinforcement direction
END
With the first line PUNC WALL" without X,Y the wall thickness D is preset to 36.5 cm for all wall punching checks. For an individual wall end near X 3.20
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Y 5.26 the check for D=24 cm is required. The third line defines that studrails are inserted at the wall end at X 8.15 to Y 2.10 and therefore no increase of the upper longitudinal reinforcement is supposed to occur. The program does not interrupt then with a design error in spite of incorrect punching. The fourth PUNC input without WALL" produces a default for the dimensions of single columns, here 40⋅40 cm.
The punching check for wall ends and wall corners may be deactivated with
PUNC WALL HEAD DUEB REIN 0.0. Then it can be checked manually.
2.4.6.
Punching Check Foundation Plates
Automatic Punching Check
Columns which stand on bedded foundation plates are indentified automatically at the punching check. They are checked with deduction of the minimal soil pressure. For this purpose the program reads the structure points from the program SOFIPLUS from the database (column dimensions) and integrates the punching force from the load cases of the superpositioned max/min internal forces of the plate. Because it is not known which soil pressure appertains to this combination, the minimum soil pressure of the superposition load cases in the punching circle is deducted for the safety. If only the load case of the maximum soil pressure is input manually in BEMESS record LC, only this load case is used then. If no load cases with bedding stresses are requested, BEMESS searches at first automatically the MAXIMA bedding results and otherwise the load case dead load.
BEMESS searches for high nodal point loads for systems from the program MONET or for ASCII inputs. In this case the column dimensions have to be defined with PUNC FOUN D 0.40 B 0.40.
Generally it is valid that the column load has to be input always at a FE node. Column loads may not be defined as an area load or a point load within an element. Otherwise the automatic punching check can not integrate a punching force.
Semiautomatic Punching Check
In order to be able to perform a punching check for foundations plates, an input at which the maximum column load has to be defined manually in the record PUNC was developed as a second variant. For the following input in BEMESS:
PUNC FOUN X .. Y .. D .. B .. P .. LC_P ..
a foundation punching check occurs at the position X,Y with the defined maximum column force P for a column with the dimension D,B. In this case the soil pressure of the load case LC_P is deducted in the circle area dK. Example:
PUNC FOUN X 3.20 Y 5.26 D 0.40 B 0.40 P 1280 LC_P 818
Like for the column punching check a from the column edge about 1/3 increased plate thickness is considered at the design of the central node. The design moment is reduced.
2.4.7.
Punching Check at a Three−Dimensional System
In increasing measure high−rise buildings are analysed according to the Finite Element Method also for three−dimensional systems. The singular column points and wall end points are a problem in the design especially for the shear design. The decisive punching points of column connections and wall ends are identified automatically also at inserted slabs and checked. Within a round cut the normal plate shear check can be omitted then. The bending moments are reduced at the columns. The decisive shear force results from the difference of the column forces over and under the slab. Because these parts are not anymore understandable from the column forces after a superposition with the partial safety factors, the punching force is integrated about the shape functions at the punching node from the bordering plate elements. The punching dimensions are extracted automatically from the column cross sections and the wall thicknesses.
In the same manner a punching check is performed for columns and wall ends at elastic bedded foundation plates with deduction of the minimum soil pressure.
In the illustration the automatically determined critical punching round cuts are plotted in red. Because the design occurred according to the DIN 1045−1, the necessary shear reinforcement is calculated in part in some round cuts. Here this is the case particularly in the foundation plate. The in each case reduced round cut is recognizable at the wall ends.
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SOFiSTiK AG − 85764 Oberschleißheim WINGRAF (V12.33−99) 7.11.2002 SEITE 1173 Durchstanzen an 3−D Hochhausdecken X Y Z Kontur −10.00 −5.00 0.00 5.00 10.00 15.00 20.00 m 5.00 0.00 −5.00 Knoten 41 V−ULS= −323.2 kN Perimeter 1 8.33 cm2 Perimeter 2 4.28 cm2 Perimeter 3 2.55 cm2 Perimeter 4 3.23 cm2 Knoten 61 V−ULS= −326.4 kN Perimeter 1 6.86 cm2 Perimeter 2 3.44 cm2 Perimeter 3 2.68 cm2 Perimeter 4 3.27 cm2 Knoten 363 V−ULS= −637.5 kN A−SS= ****** Knoten 373 V−ULS= −1193 kN Perimeter 1 18.2 cm2 Perimeter 2 7.53 cm2 Knoten 383 V−ULS= −576.0 kN Perimeter 1 12.7 cm2 Perimeter 2 6.28 cm2 Perimeter 3 5.10 cm2 Perimeter 4 6.22 cm2 Knoten 683 V−ULS= −581.1 kN Perimeter 1 16.2 cm2 Perimeter 2 8.39 cm2 Perimeter 3 4.89 cm2 Perimeter 4 6.19 cm2 Knoten 693 V−ULS= −1206 kN Perimeter 1 18.6 cm2 Perimeter 2 7.79 cm2 Knoten 703 V−ULS= −573.2 kN Perimeter 1 12.6 cm2 Perimeter 2 6.21 cm2 Perimeter 3 5.10 cm2 Knoten 1003 V−ULS= −280.3 kN Perimeter 1 6.44 cm2 Perimeter 2 2.87 cm2 Knoten 1013 V−ULS= −594.4 kN Perimeter 1 13.3 cm2 Perimeter 2 6.70 cm2 Perimeter 3 5.10 cm2 Perimeter 4 6.22 cm2 Knoten 1023 V−ULS= −319.2 kN Perimeter 1 6.40 cm2 Perimeter 2 3.09 cm2 Perimeter 3 2.68 cm2 Knoten 1262 V−ULS= 386.9 kN Perimeter 1 9.54 cm2 Perimeter 2 3.75 cm2 Knoten 1322 V−ULS= 345.2 kN Perimeter 1 7.62 cm2 Perimeter 2 2.12 cm2 Knoten 1402 V−ULS= 183.4 kN Perimeter 1 4.12 cm2 Perimeter 2 1.11 cm2 Knoten 1483 V−ULS= 191.2 kN Perimeter 1 4.48 cm2 Perimeter 2 1.71 cm2 Knoten 1582 V−ULS= 112.1 kN A−SS= 0 cm2 Knoten 1874 V−ULS= 551.2 kN A−SS= 0 cm2 Knoten 1884 V−ULS= 235.6 kN A−SS= 0 cm2 Knoten 2174 V−ULS= 553.4 kN A−SS= 0 cm2 Knoten 2184 V−ULS= 234.5 kN A−SS= 0 cm2 Knoten 2474 V−ULS= 246.3 kN A−SS= 0 cm2 Knoten 2484 V−ULS= 111.1 kN A−SS= 0 cm2 Knoten 2723 V−ULS= 383.7 kN Perimeter 1 9.39 cm2 Perimeter 2 3.64 cm2 Knoten 2783 V−ULS= 336.4 kN Perimeter 1 7.21 cm2 Perimeter 2 2.12 cm2 Knoten 2863 V−ULS= 181.0 kN Perimeter 1 4.01 cm2 Perimeter 2 1.11 cm2 Knoten 2944 V−ULS= 187.8 kN Perimeter 1 4.32 cm2 Perimeter 2 1.11 cm2 Knoten 3043 V−ULS= 116.1 kN A−SS= 0 cm2 Knoten 3335 V−ULS= 537.3 kN A−SS= 0 cm2 Knoten 3345 V−ULS= 240.1 kN A−SS= 0 cm2 Knoten 3635 V−ULS= 546.9 kN A−SS= 0 cm2 Knoten 3645 V−ULS= 239.1 kN A−SS= 0 cm2 Knoten 3935 V−ULS= 247.2 kN A−SS= 0 cm2 Knoten 3945 V−ULS= 115.0 kN A−SS= 0 cm2Durchstanzen, Bemessungsfall 1 (Max=33.0)
The program BEMESS may carry out now additionally a stress amplitude check. If the stress amplitude is exceeded for the defined load cases, the reinforcement is increased automatically until the check is correct. The link stress for the full shear consideration with 45 degree diagonal strut inclination is determined for the stress amplitude of the shear reinforcement.
2.5.
Stress Determination
.
Stresses of the single load cases or of the single load cases from superposition may be printed directly without the program BEMESS with the program WINGRAF at cuts or isolines.
The option of the stress determination in BEMESS is used for the search of extreme stresses from a series of load cases. In this case BEMESS selects itself the maximum stress from the indicated load cases for each element. Then a plot of this extreme stresses shows in general results of different load cases like a moment envelope.
The normal stresses are determined according to the formula: s + N
A" MW (1)
This is done separately for the two sides of the plate or the shell for σx, σy and σxy. These can be used for the calculation of the principal stresses σI and σII
and the angle α.
The shear stress at the plate centre or shell centre is calculated according to the formula:
t + 1.5 @ V
A (2)
The design shear force V is the maximum shear force determined at the design point by means of geometric addition of the shear forces VX and VY:
V +
ǒ
V2x) V2yǓ
1ń2(3) Also von mise stresses on top, on bottom and as maximum values are calcu-lated. To get the maximum von mise stress also inside an element, the el-ements are cut into 10 layers for the sigv analysis.
The stress determination with BEMESS must not be used after a material non−linear calculation with ASE, because the formula σ = N/A M/W is not valid anymore for the structure thickness of a non−linear stress distribution! Non−linear stresses can be requested with the program WING in a separate way.
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3
Input Description
.
3.1.
Input Language
The program BEMESS uses the CADINP input language, see general man-ual SOFiSTiK: ’FEA / STRUCTURAL Installation and Basics’.
3.2.
Input Records
The following records are defined: Records Items
CTRL
CRAC MREI NSTR
TYPE RMOD SYST WALL AUGM GALF THIC TENS LCR
PFAI RO_V ROBU COTT FACH WARN LCRI VF70 SNIP
WINT WEND REDN RADP
MUEZ XMIN DDES STAN WK BETA BOND BET1 BET2
K1 DDEB WKB
FFCT KC K ROBU PARA
SIGS SIGT CHKC CHKS FATC LS_U LS_L LS_V LS_P
FACU FACL FACV FACP SIGP LOCP
MAT CONC STEE K BETZ N MINC MSTA T011 T02
T03 AM3 FC FY TU0 TUGR TRD SC1 SC2
SS1 SS2 GEOM GEO DIRE THRE PARA PUNC
H HA DHA HB DHB DDHA DDHB HPRE
H HA DHA HB DHB DDHA DDHB HPRE
UPP LOW TYPE X Y Z
ABEX ABMI ABIN BEEX BEMI BEIN
NOG NOEL DU DU DU3 DL DL2 DL3 WKU
WKU2 WKU3 WKL WKL2 WKL3 SSU SSU2 SSU3 SSL
SSL2 SSL3 ASU ASU2 ASU3 ASL ASL2 ASL3 BSU
BSU2 BSU3 BSL BSL2 BSL3 TYPE
TYPE X Y Z D B HEAD DHEA RO_V
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Records Items LC GRP ELEM NODE S NO PERCNO ENVA ENVB WKU WKL SIGU SIGL
FROM TO DELT ENVA ENVB WKA WKB SIGA SIGB
FROM TO DELT ENVA ENVB GROU WKA WKB SIGA
SIGB
NO NO1 MX MY MXY VX VY NX NY
NXY
ECHO OPT VAL
The input sequence of the input records is arbitrary. However, END must al-ways be the last input record. Each ELEM or NODE record causes a design with the already defined parameters (possible as the default values). An input of GEO or DIRE or THRE after ELEM/NODE refers thus always to the next design specifications.
The records HEAD, END and PAGE are described in the general manual SO-FiSTiK: ’FEA / STRUCTURAL Installation and Basics’.
A reasonable analysis is possible even without data. The default values are activated in each case.
See also: MREI CRAC NSTR MAT PUNC
3.3.
CTRL − Control of the Design
ÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄÄÄ
CTRL
Item Description Dimension Default
TYPE
RMOD
Design task
SERV Reinforced concrete design, for loadcases on SLS level STRE Stress calculation according
to theory of elasticitiy
ULTI Reinforced concrete design, for loadcases on ULS level SLS SLS design checks
−> MREI, CRAC or NSTR
default: in dependence on the system Save mode for reinforcement or stresses:
SING Single analysis, no save SAVE Save, does overwrite already
stored values
SUPE The maximum of the calcula− ted and the already stored reinforcement is saved.
ADD The calculated reinforcement is added to the one stored in the data base. Prefabricated parts with subsequent sup− plementing by cast−in−place concrete can be designed in this way.
LIT
LIT
*
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Item Description Dimension Default
SYST
WALL
AUGM
Design strategy (required or allowed for external forces and moments only)
SPAC Shell design GIRD Plate design FRAM Disk design Deep beam
(see also record MAT AM3)
YES Requirements for minimum reinforcement
0.05% per side for DIN 1045−1988
0.075% per side for DIN 1045−1
0.10% per side for OENorm B 4700
0.15% per side for EC2, BS,ACI
(Default for disks)
NO No minimum reinforcement (Default for shells)
Small member thickness
YES For h < 7cm the internal for − ces are increased by calcula− tion according to
DIN1045 −1988, 17.2.1 (6). NO No correction of the internal
forces or the permissable stresses due to the small member thickness LIT LIT LIT SPAC * YES
Item Description Dimension Default GALF THIC TENS LCR PFAI
Global load safety factor
All internal forces for the design accord-ing to DIN 1045−1,EC2,BS,ACI + OE-NORM in BEMESS are multiplied by the load safety factor GALF. Default:
CTRL SERV GALF=1.45 for DIN 1045−1, EC2, OENORM,EHE
GALF=1.55 for BS,ACI
CTRL ULTI GALF=1.0
CTRL CRAC GALF=1.0 Strict compression zone check
SEPA Check in two seperate directions
FULL Strict check
Reduction of the permissible concrete compressive stress at transverse tension (May be defined 0 %)
default 20%,
(DIN 1045−1 + DIN−Fachbericht: 25%) Reinforcement distribution number Compression failure method for shells and disks
1 mechanical correct analysis 2 does always transform into
compression reinforcement (refer to Basics−Reinforce− ment Concrete−Disks) − LIT % − − * SEPA * 1 1
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Item Description Dimension Default
RO_V
ROBU
COTT
FACH
Maximum reinforcement for shear for normal slab region (see also PUNC ro_v for punching region).
Check of a minimum reinforcement for the safety of a ductile member behaviour (robustness reinforcement)
FCTM according to DIN1045−1 with a crack moment due to the concrete tensile strength fctm FCTK or check with fctk
or input of a different strength
Caution: ROBU will be omitted here in future. See record MREI
Limitation of the cotangens theta for shear design
input permissible between 1.00 and 3.00 for DIN 1045−1 and EHE
default for database according to DIN− Fachberichte: 7/4 in accordance with in-troductory decree
German DIN Fachberichte
0 No consideration
1 Consideration of additional design codes according to the DIN Fachberichte, minimum value for VRd,ct in the shear check without computed necessary shear reinforce− ment
default: according to the design code in the database − N/mm2 − − 0.2 − * 0
Item Description Dimension Default WARN LCRI VF70 SNIP WINT WEND REDN RADP
Special error messages can be switched off. Possible for error no. 77, 78 and 207. Determination of the reinforcement maximum from some design calculations Factor for increase of the load bearing ca-pacity for accidental loading situation Building factor γb2 of the SNIP 2.03.01 Wall integration length for punching check
default: 2.0
für DIN 1045−1988 1.5 Punching at wall ends
Default: according to the standard Factor for design with reduced normal force
Factor the modification of the check ra-dius for punching
− − − − − − − − * − 1.0 0.9 2.0 (1.5) * 1.0 6.0
With CTRL TYPE ULTI can be defined, that the load cases contain internal forces and moment in the ultimate limit state. The default for CTRL ULTI is defined in the following manner: If the superposition occurs with actions for the design state in program MAXIMA, this is recognized by BEMESS. The program uses the load cases as load cases with ultimate limit loads also with-out an input CTRL ULTI.
With GALF the load cases can get a factor for the design according to the EuroCode 2. If already a load case superposition occurred including the par-tial safety factors of EuroCode 2 with the program MAXIMA, CTRL ULTI with CTRL GALF=1.0 is to be used. ULTI means that the design load cases already represent ultimate loads and they do not have to be provided with any additional load safety coefficients. If MAXIMA has not determined any load case combinations in accordance with EuroCode 2, this can be done approxi-mately in BEMESS. SERV implies an average value between 1.3 for g loads
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and 1.5 for q loads. Any arbitrary value can be input additionally for GALF. The input for GALF has no importance for DIN1045−1988.
The literal CTRL TYPE CRAC can be used for the identification of a pure BE-MESS service load check. In this case the load safety factor CTRL GALF is used with 1.0. Additionally no check for the ultimate limit state, no shear de-sign and no punching check are printed. The function CTRL TYPE CRAC is only possible in connection with the option CTRL RMOD SUPE to complete a previous design in the ultimate limit state. Because data about the punch-ing are also necessary for the service load check, e.g. support moment reduc-tion over the column, the punching check should be activated for a pure BE-MESS service load check. In this case the load cases of the program MAXIMA has to be defined with the maximum support reactions of the service load superposition! However, for CTRL SLS the punching is considered, but it is not saved to avoid an influence of the failure results which are determinent for the punching, e.g. for the program WING. A shear check does not occur for CTRL SLS.
Compression zone thickness − strict method:
If a plate has a crack at its lower side and a 90 degrees rotated crack at its upper side (twisting moments at the plate corners), the compression zone thickness can be kept perpendicularly to each crack. This case is considered correct by CTRL THIC SEPA. Since, however, the compression zones do not pass through the middle, the cracks meet at the interior. The strict check reports this case by an error message as not admissible. Consider, that al-most none finite element analysis can manage without an error message for the minimum thickness check of the compression zone (twisting moments always arise at some place without sup-porting axial forces).
The check in separate directions occurs as the default (CTRL THIC SEPA). A reinforcement increase is performed only in these directions.
The strict check must be requested explicitly by CTRL THIC FULL.
For shear checks according to DIN 1045−1, EC2, ACI and British Standard it is possible to input a maximum percentage of reinforcement RO_V. If the
normal shear check without shear reinforcement is not possible with the rein-forcement determined from the bending, the program attempts to increase the bending reinforcement ratio without an use of a shear reinforcement. This succeeds mostly, particularly in the area of the moment zero points. In this case the bending reinforcement is increased up to a maximum reinforce-ment ratio RO_V in percent.
Punching at wall ends:
To get more to the save side, the integration length has been set to 2*wall width. Following input is possible e.g. with:
CTRL WINT 2.00 wall integration length 2.0*wall width (default 2.0, DIN1045−1988: 1.50) CTRL WEND 0.70 wall end perimeter reduction/increase
The shadowing area may be input for the punching at wall ends with CTRL WEND for the adaptation to other standards or conditions. E.g. CTRL WEND 0.7 defines the use of maximum 70 % of the full round cut. In this example 30 % = 108 degree are shadowed. If this factor is input larger than 0.8, the in-creasing factor β for non−axisymmetric loading is set to at least 1.4. (See
Chapter 2)
The check of a minimum reinforcement for the safety of a ductile member be-haviour (robustness reinforcement) occurs with an input for ROBU (at this time only for two−course reinforcement). The check according to DIN1045−1 with a crack moment due to the concrete tensile strength fctm is performed with CTRL ROBU FCTM. However, a different tensile strength may be input with CTRL ROBU, e.g. CTRL ROBU 2.50 (N/mm2). The crack moment can be converted into a necessary minimum reinforcement with a fixed lever arm value kz=0.9 and the steel yield strength fyk.
Superposition of various design calculation with LCRI
With CTRL LCRI ... it is possible to determine the reinforcement maximum (incl. punching reinforcement) from some previous design calculations. This maximum can be used then as basis for the current calculation. The current calculation is saved with the reinforcement distribution number which is de-fined with CTRL LCR. CTRL RMOD SUPE is activated automatically. It is also possible to generate the maximum in a BEMESS calculation without further analysis, e.g.:
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prog bemess head ctrl LCRI 1,2,3,4 ctrl LCR 11 endSee example: DIN_FB_Platte.dat
If two designs in ultimate limit state or two checks for serviceability are done with the in each case same LCR number, then the results only of the last cal-culation are saved always in the database.
VF70 − Factor for increase of the load bearing capacity for accidental loading situation
For power plant design the shear capacity according to DIN 1045−1 equation 70 and 105 can be increased by a factor with CTRL VF70, e.g. VF70=1.15. to take into account a reduction of the partial safety factor for these checks REDN − Factor for design with reduced normal force
A design with reduced normal forces is possible with CTRL REDN . To design also maximum tension and maximum pressure, in any case a previous run without REDN is necessary! Thus this option is only allowed with parallel CTRL RMOD SUPE! To study the influence of REDN in LCR1−LCR2, the best way is to use:
PROG BEMESS
HEAD Design without reduction CTRL LCR 2
... END
PROG BEMESS
HEAD Design with reduced normal forces CTRL LCR 1 LCRI 2 RMOD SUPE
CTRL REDN 0.8 ...
END
It is also possible to processed both BEMESS parts with LCR 1 (without input for LCR).
The check radius for punching perimeters can be modified with CTRL RADP. Sectors with openings or boundaries closer than 6⋅d to the column edge do not act in the perimeter by default. With RADP this factor can be changed (de-fault 6.0 for thin slabs, intern already reduced for thick slabs).
