Check of details and bearing areas

The target of this project is to verify bearing areas of prefabricated concrete elements and check end zones of elements. The end zone of a beam is checked using the Strut-and-Tie analysis (SaT).

The checks of bearing areas are based on chapter 10.9.5 from EN 1992-1-1.

Fig. 1 Figure 10.6 from EN 1992-1-1

The check of the end zone (anchorage) is based on figure 6.27 and chapter 10.9.4.7 for anchorage of reinforcement in the support (EN 1992-1-1). But we could say that both checks are described in the code very shortly and many various cases are not stated there.

Fig. 2 Figure 6.27 and 10.5 from EN 1992-1-1

Special ULS checks of details of a concrete simply supported beam were implemented in this project.

Although the functionality was implemented for both Frame XYZ and XZ, the internal forces and loads are assumed in one plane XZ of the local coordinate system of beams. The types of the details are restricted to local support areas at the ends of beams. A procedure for calculation of internal forces and checks based on the Strut-and-Tie (SaT) model is described in this document.

The project was split to two basic parts:

• Check of bearing areas – verification of the defined dimension of a bearing
• Check of details – SaT analysis of a standard beam end-zone (SBEZ)

Definition of terms

The following terminology should be clear to the users who want to use this module. All values are explained on the Non-direct detail.

• Supported member – member which is supported; it is part of the structure
• Supporting member – member which supports the structural member; it can be fictive or real
• Interface material – material between supported and supporting member, bearing material
• Length of support (a) – it is total length of the support
• Effective length of support (a₁;b₁) – it is the length of the support, which is able to carry load from the supported member
• Ineffective length of the supporting member (a₂) – it is the distance from the edge of the supporting member to the effective length of the support
• Ineffective length of the supported member (a₃) – it is the distance from the edge of the supported member to the effective length of the support
• Tolerance of supporting member Δa₂
• Tolerance of supported member Δa₃
• Partial tolerance for calculation of design value of supporting member Δa₂/
• Partial tolerance for calculation of design value of supported member Δa₃/

Fig. 3 Explanation of values in end zone

Before we can solve the issues related to SaT we have to define the details with their bearing areas checks.

Check of bearing areas - Standard Beam End Zone (SBEZ)

The program supports three basic types of standard beam end zone. These types are defined by the user using the SBEZ data:

Direct dry	direct contact between two members without interface material
Direct wet	direct contact between two members with wet interface material (mortar or concrete)
Non-direct	another element is inserted between the supported and supporting member; the element can be concrete, steel, neoprene....

Fig. 4 Three basic types of SBEZ

Check of details - why do we use SaT analysis

Each concrete structure could be divided to two groups of regions. The design of B (Bernoulli or Beam) region is well understood and the entire flexural behaviour can be predicted by simple calculation. On the other hand, even for the most often used examples of D (Disturbed or Discontinuity) regions (such as end zone, deep beams or corbels), engineer's ability to predict the capacity is either poor (empirical) or requires substantial computation effort (finite element analysis) to reach an accurate estimation of the capacity. Examples of the discontinuity areas are shown in the figure.

Fig. 5 Typical examples of the B and D regions

Definition of details

The concept of data definition is very similar to connections in steel structures. Additional data are defined in the structure and then the data check themselves. No additional check service is needed.

There are new items in the Concrete Advanced tree.

SaT details

Support zones	definition and check of one detail
Check of details	check of all details in the project

Fig. 6 Concrete tree

Procedure for definition of SBEZ data

Because this check is very different from other standard concrete checks, the procedure of working with the SBEZ data is described in the following points. The following procedure must be followed strictly:

Definition of stages if SBEZ data are required in some stage

User selects SBEZ detail from the concrete tree

Property of SBEZ data dialog appears

User defines property of the SBEZ detail – combination, position of details, type of detail

User selects the beam where SBEZ data are defined on

After definition of data the following condition has to be satisfied:

• Support has to exist in the user defined position of the detail
• Support has to exist in the user defined construction stage
• Support has to be at the end of the beam – SBEZ data are not possible on intermediate support

When the conditions above are not fulfilled, then the warning is given to the user: “The detail doesn’t correspond to the structure, no support was found in selected section.”

The data are displayed in the 3D window with their own view flag

Fig. 7 SBEZ data defined on the beam in 3D window

User selects the SBEZ data and using the refresh button the check of bearing areas and the check of detail are performed.

Property of the SBEZ data

The properties of the detail are divided to three parts:

Load	selection of the type of load and of the appropriate load case, combination or class
Geometry on the beam	position of the SBEZ data on the beam
Support parameters	will be explained in the following chapter

Fig. 8 Property of the SBEZ data

Support parameters

The properties of the detail (support parameters) depend on the type of the selected detail.

Type of detail - We distinguish three basic types of SBEZ details:

• Direct dry
• Direct wet
• Non-direct

Some values in Support parameters are filtered according to the selected type of detail. They are shown in the next table.

Property depending on type of support	Direct-dry	Direct-wet	Non-direct
a - Length of support	x	x	x
a1; b1 - Effective length and width of the support			x
a2 – Ineffective length of the support			x
Interface material (neoprene, mortar....)		x	x

Tab. 1 Property depending on type of support

Type of support – the type of support is necessary for the calculation of the minimum dimension of the detail according to tables 10.2 and 10.3 from [1].

Standard EN 1992-1-1

• Line support
• Purlins (concentrated)
• Ribbed floors (concentrated)
• Concentrated support

Definition of support width – the program is able to read dimension of the detail directly from the support dimensions; There are values a and b in case of Non-direct support

Point support – width of support is a = b

Fig. 9 Setting for temporary support

Beam, column – dimensions of elements a = b are dimension of the beam (column)

Type of support	a	b	a1; a2	b1
Direct dry	read	a	-	-
Direct wet	read	a	-	-
Non-direct	read	a	user defined	user defined

Tab. 2 Dimension of support for point support

Type of support	a	b	a1; a2	b1
Direct dry	read	read	-	-
Direct wet	read	read	-	-
Non-direct	read	read	user defined	user defined

Tab. 3 Dimension of support for beam, column support

Material of interface – it is necessary for calculation of bearing material strength

Type of support	Concrete	Steel	Mortar	Neoprene
Direct dry
Direct wet	x		x
Non-direct	x	x		x

Tab. 4 Dimension of support for beam, column support

Materials Mortar and Neoprene are not available in SCIA Engineer.

Material of supporting member – it is necessary for the calculation of the minimum allowed ineffective length of the support from table 10.3 from [1].

Type of support	Concrete	Steel	Masonry
Direct dry	x	x	x
Direct wet	x	x	x
Non-direct	x	x	x

Tab. 5 Material of supporting member

Material Masonry cannot be used in SCIA Engineer.

Sum of tolerances – the program distinguishes between two calculations of tolerances (see 3.1.3)

• Algebraic
• Quadratic

Precast support – this option appears only for supporting material concrete; it is needed for the calculation of deviation Δa₂ (see table 10.5 [1].)

Values r₂ and c₂ - the values of the radius of reinforcement and concrete cover are related to the supporting member; they are available only for concrete as the material of supporting member

Material of support	r2	c2
Concrete	x	x
Steel
Masonry

Tab. 6 Definition of radius and cover of supporting member depending on material

Bearing pressure uniform (10.9.5.2(3)) - When check box is switched OFF, then value b₁ is limited by 600 mm. Higher value cannot be used for the calculation.

Isolated members (10.9.5.3(1)) - When this check box is switched ON in, then values in tables 10.2-10.4 will be increased by 20 mm.

• This check box is not available when line support is selected

Direct dry

Dimensions of direct dry support are defined only by the total length (a) of the support. Other parameters are calculated automatically.

Fig. 10 Direct dry support

Direct wet support

Dimensions of direct wet support are defined only by the total length (a) of the support and by material of the interface. Other parameters are calculated automatically.

Fig. 11 Direct wet support

Non-direct support

Dimensions of non-direct support are defined by the total length (a) of the support and effective dimensions (a₁; b₁) of support and ineffective length of the support (a₂). The ineffective length of the supported member (a₃) is calculated automatically.

Fig. 12 Non-direct support

Limitation for definition of support

The following conditions should be fulfilled during definition of SBEZ data or during changes of SBEZ data in the property dialog. The limitation also depends on the type of support.

• A support has to exist in the user defined position of the detail
• A support has to exist in the user defined construction stage
• A support has to be a nodal support – SBEZ data are not possible on intermediate supports

Temporary support

The temporary support is the support which is removed during construction stages. It is recognized automatically. When the support is temporary, then user defined value a is equal to value a₄. The value a₄ is measured from the end of the beam on which the SBEZ data are located. The following condition has to be fulfilled.

Is the support temporary or not? If YES then

x_sup ≤ a₄

where,

x_sup is the x coordinate of the SBEZ data.

Fig. 13 Bearing length for temporary support

Direct wet or dry support

For the final direct wet or dry support the following conditions are calculated. The minimal value of a₂ (from table 10.3 [[1]]) and maximal value a₃ (from table 10.4 [[1]]) are determined. The value a_1,lim is calculated during the user definition of SBEZ data and it is checked each time when value a is changed in the SBEZ data.

a_1,lim = a – (a_2,min + a_3,max)

The limitation during the definition of SBEZ data is:

a_1,lim + a_3,max ≥ x_sup ≥ a_3,max

Fig. 14 Bearing length for direct dry or wet support

Non-direct support

The same verification as for the final direct dry or wet support is performed for non-direct support, but value a_1,lim is not calculated, because values a₂ and a₃ are known as user defined values.

The limitation during the change of the defined SBEZ data is:

a₁ + a₃ ≥ x_sup ≥ a₃

Fig. 15 Bearing length for non-direct support

Check of bearing areas

Calculation of nominal, design values and tolerances

The user defines nominal dimensions of details (a, a₁, b₁…). Checks of bearing areas are performed using design values of dimensions, which take into account tolerances and “inefficient” parts of the concrete. Design values of the support are marked with subscript d. There are little different design values for the check of bearing areas and for the checks of detail (SaT).

Direct wet / dry support - nominal, design values and tolerances

Value a is defined by the user, no check will be performed and values a₂ and a₃ come from tables 10.3 and 10.4 EN 1992-1-1 as minimal recommended values and a₁ is calculated. Value a₂ is determined from table 10.3 for Ed = f_Rd (for f_Rd see 3.2.1).

Value n depends on the type of tolerances set in parameters of detail.

• Algebraic – n = 1
• Quadratic – n = 2

Tab. 7 Nominal and design values of direct support

Fig. 16 Nominal and design values of direct support

Non-direct support - nominal, design values and tolerances

Values a, a₁, a₂ are defined by the user, and value a₃ is calculated. Value a₁ is without tolerance because it is fixed value.

Tab. 8 Nominal and design values of non-direct support

Fig. 17 Nominal and design values of non-direct support

Calculation of tolerances

The tolerances are calculated automatically by the program. It is possible to select the way of calculation of tolerances (algebraic, quadratic) in the SBEZ data (see 2.2.1).

Tolerance of supporting member Δa₂

Tolerance Δa₂ is determined according to table 10.5 from [[1]].

Tab. 9 Recommended values for tolerance Δa₂

A precast or cast-in-place support is determined according to check box. Precast support in the SBEZ data see 2.2.1 (this option appears only if concrete material is selected as supporting material.

Masonry material is not available in the current version of the program.

Value L in the formulas above is the length of the span. The length of the span is determined automatically by the program depending on the existence of the “continuous beam” object.

• Continuous beam is used. The detail is defined on the beam and the program determines the length of the span where the SBEZ data are defined. The spans are automatically updated according to construction stages on the continuous beam.
• Continuous beam is not used, then it is the distance between two neighbour active supports near the member where the SBEZ data are defined.

Tolerance of supported member Δa₃

Tolerance Δa₃ is determined according to 10.9.5.2(1) from [[1]].

Δa₃ = L_n / 2500

Where

L_n is the length of the member. Length of the member is automatically determined by the program depending on the existence of the members. It is the length of the longest member in the selected stage between active supports, where the data are defined.

Check of bearing areas and strengths

For the proper function of the bearing areas several checks have to be satisfied. These checks are focused on the limited dimension of the bearing and limited strength in the bearing. Following checks are performed

• Check of bearing strength σ_Ed/f_Rd (10.9.5.2(2))
• Check of bearing length a₁(10.9.5.2 – Table 10.2)
• Check of ineffective distance from outer end of supporting member a₂ (10.9.5.2 – Table 10.3)
• Check of ineffective distance beyond outer end of supported member a₃ (10.9.5.2 – Table 10.4)
• Check of minimal bearing length for temporary support a₄ (only for DTU 4.3)

Not all checks are done for each type of detail. The checks are performed according to the type of support as follows

Check	Direct wet / dry	Non-direct
Bearing strength	x	x
a1	x	x
a2		x
a3		x
a4	x

Fig. 18 Check performed according to type of detail

Check of bearing strength

The bearing stress (σ_ed) is calculated from the acting reaction in the support and verified against bearing strength (f_Rd) calculated according to 10.9.5.2 (2). The bearing stress σ_ed is calculated using the following formula.

σ_ed = F_Ed / (a_1d.b₁)

Where,

F_Ed is the support reaction

a_1d, b₁ – design value of length and nominal value of width

The bearing strength f_Rd is determined by following formulas

Direct dry

f_Rd = 0,3* f_cd for Direct dry (see 10.9.4.3)

Non-direct

interface material – concrete, steel, neoprene

f_Rd = 0,4* f_cd

interface material – mortar

f_Rd = f_bed ≤ 0,85*f_cd

Neoprene and Mortar materials are not available in the current version of the program.

Where,

f_cd is the lower of the design compressive strengths for supported and supporting member –time dependant value

f_bed is the design compressive strength of bedding material – interface material defined by the user

The result is Check value = σ_ed/f_Rd

If σ_ed/f_Rd ≤ 1,0 — OK

If σ_ed/f_Rd > 1,0 — NOT OK, “Bearing design stress is higher than bearing strength according to table 10.9.5.2 EN 1992-1-1”

FEd	acting reaction
σed	bearing stress
fRd	bearing strength
Checkcalc	calculated value σed / fRd
Checklim	limited value from concrete setup, default 1.0
a1,d	design value of bearing length
a1,rec	recommended value of bearing length

The following values are available in the Table composer: a₁; b₁; f_cd; f_bed

Check of bearing length (a_1d)

Verification of distance a_1d with recommended value a_1,rec depending on ratio of σed/f_cd according to table 10.2 is performed. For direct support we calculate value a_1d and check it against table 10.2. For non-direct support we check value a_1d against table 10.2.

Tab. 10 Nominal and design values

Values a₂ and a₃ for direct wet or dry support are determined from table 10.3 or 10.4 [1]. Calculation of σ_ed is performed in chapter 3.2.1.

σed/fcd	≤ 0,15	0,15 – 0,4	> 0,4
Line support	25	30	40
Support of Ribbed floors and Purlins	55	70	80
Concentrated support	90	110	140

Tab. 11 Recommended value a_1,rec from table 10.2 [1].

Effects of isolated members (10.9.5.3(1))

When this check box is switch ON in the SBEZ data, then values in the table above are increased by 20 mm

This check box is not available when a line support is selected.

The result is Check value = a_1,rec/a_1d

If a_1,rec/a_1d ≤ 1,0 — OK,

If a_1,rec/a_1d > 1,0 — NOT OK, “Net bearing length is less than minimum value according to table 10.2 EN 1992-1-1 it is necessary to increase net bearing length”

The following values are available in the Table composer: a₁; Δa₂;Δa₃,f_cd; σ_Ed

Check of ineffective length (a_2d) of supporting member

Verification of distance a_2d according to table 10.3 is performed only for non-direct support. For direct wet or dry support value a_2d is determined from table 10.3 from [[1]] according to 10.9.5.2 (1)

Material of support	Type of support	≤0,15	0,15-0,40	>0,40
Steel	Linear	0	0	10
	Concentrated	5	10	15
Reinforced concrete fck ≥ 30 MPa	Linear	5	10	15
	Concentrated	10	15	25
Plain and reinforced concrete fck < 30 MPa	Linear	10	15	25
	Concentrated	20	25	35
Masonry	Linear	10	15	Message; 25
	Concentrated	20	25	Message; 35

Tab. 12 The recommended value a_2,rec from table 10.3 [1] depend on the ratio σed/f_cd.

In case of ratio > 0,4 and support material masonry, the message to the user is issued and values as for concrete f_ck < 30 MPa are used.

WXXX – “The concrete padstone should be used for this material of support and ratio of stresses according to table 10.3 EN 1992-1-1.”

The result is Check value = a_2,rec /a_2d

If a_2,rec /a_2d ≤ 1,0 — OK

If a_2,rec /a_2d > 1,0 — NOT OK; “Ineffective distance beyond outer edge of supporting device to the edge of the effective area of the support is too small according to table 10.3 EN1992-1-1. It is necessary to increase value a₂”

The following values are available in Table composer: a₂; Δa₂; Δa₃, Δa₂/; Δa₃/, f_cd; σEd

Check of ineffective length (a_3d) of the supported member

Verification of distance a_3d according to table 10.4 is performed only for non-direct support. For direct wet or dry support value a_3d is determined from table 10.4 [[1]]. Value a₃ is determinated from the user-defined geometry of the structure. This value is compared with recommended value a_3,rec from the code table 10.4 [1].

The values from table 10.4 depend on reinforcement in the supported member.

Detailing of reinforcement	Line support	Concentrated support
Continuous bars or strand over support	0	0
Straight bars or strands	5 mm	max(15 mm; c3)
Strands or bars “go out” from the beam	5	15
Vertical hooked bars or strands	15 mm	c3 + R3

Tab. 13 Recommended value a_3,rec - EN 1992-1-1

c3	Concrete cover of supported member
r3	Radius of reinforcement of supported member

The 1st row in the table is used only for the internal support, not in the case of the end support.

When straight bars and hooks exist together, then the higher value will be taken into account.

Limitations - the formulas in setup are not available in the current version of SCIA Engineer.

The result is Check value = a_3rec /a_3d

If a_3rec /a_3d ≤ 1,0 — OK

If a_3rec /a_3d > 1,0 — NOT OK “Ineffective distance beyond outer edge of supported member to the edge of effective area of the support is too small according to table 10.4 EN1992-1-1”.

The following values are available in a₃; Δa₂; Δa₃, Δa₂/; Δa₃/

Concrete setup for check of bearing areas

There are new tables according to EN1992-1-1 in concrete setup. This part is situated under Concrete > ULS > Details. This part of the setup is split to two tabsheets.

• Bearing checks
• Anchorage checks

There are tables 10.2, 10.3, 10.4 adapted from [1] where recommended minimal values can be changed by the user.

Fig. 19 Concrete setup for Bearing areas

Strut and Tie analysis of SBEZ

The procedure treats each reinforcement layer separately. A concrete strut is associated with each layer, corresponding to its anchorage capacity. Struts are “piled up” until the required force (design shear force) is reached.

The check is performed for prestressing and soft reinforcement together. If the existing reinforcement is not sufficient for that, new reinforcement is added and the check of struts starts again from the beginning. This is repeated until the obtained reinforcement layout is satisfying.

Only when it is not possible to add anchorage reinforcement in order to carry the required force (i.e. there is no space left for additional reinforcement) an error message is issued.

The following terms should be clear to users working with this module. All values are explained in the following table.

Sign	Formula	Description
Zlit	Program determination	level of current reinforcement layer
Lstrut	See §4.1.2	width of the strut
θm		average value of strut angle
Zinf	Zlit = Zinf; usually for the first layer, then Zinf,(i+1)=max{Zsup(i); Zlit(i+1)}	level of the lower fibre of the compression zone
Zsup,max	Zsup,max=min{Zlit + Lstrut*tgθm;Zmax}	max possible level of the upper fibre of the compression zone (depends on Lstrut)
Zsup	Zsup = min(Lstrut * tg(θm) + zinf ;Zsup,max)	actual level of the upper fibre of the compression zone
Zmax	Zmax = h – 0,1*h	maximum possible height of the struts; limited by cross-section height
Ac,strut	Ac,strut = b * (Zsup - Zinf)	area of compression zone;
σRd,max	σRd,max = k2n´ fcd	max compression stress in concrete strut
Fcd,max	Fcd,max = Ac,strut * cos(θm)*sRd,max	max compression force in concrete strut
Fs	Fs(i) = As ss Fs(i) = Ap sp	max force in reinforcement layer (capacity of i reinforcement layer)
Fs,max	see §4.2.3	Useful force (or limit force) in reinforcement layer “after reduction”
Ratio	Fs,max /Fs	capacity of layer from the point of reinforcement tie
Reserve	(Fcd,max –Fst,max) / Fcd,max	capacity of layer from the point of concrete strut

Determination of the strut parameters

The parameters of the strut should be determined before the execution of the anchorage check. It is necessary to calculate the design value of the support length a_1d and the length of the strut L_strut. The design support length is calculated by the different way as for the check of bearing areas.

Determination of design value a_1d for anchorage check

The design value a_1d is calculated for each reinforcement layer because the parameters of the layer can be different, but the program calculates the a_1d of the first reinforcement layer and this is taken into account also for another layer.

The design values a_1d are different from the values defined for the bearing check. Only the calculated tolerances are taken from the chapter 3.1.3 as for the bearing checks. The design length of the support (a_1d) is calculated according to the type of the support in accordance with figure 10.5 from [1].

Direct wet/dry support

Fig. 20 Value a_1d for anchorage check for direct support

Non direct support

Fig. 21 Value a_1d for anchorage check for non direct support

Determination of the length of the strut - L_strut

The length of the strut is determined according to the type of the support. The design value (a_1d) is the initial value for determination of the length of the strut (L_strut). For the determination of L_strut the following quantities are used

• Dispersion cone from a_1d.
• Position of points A and B

a) Dispersion cone

The program distinguishes between the following types of dispersion cone disp:

Direct bearing – vertical 90 degrees

Non-direct support - default 45 degrees,

• the angle must be used symmetrically on both sides of the cone (because of equilibrium),
• the angle must be adapted (taken greater that 45 degrees) in the case that the cone does not reach the straight part of the reinforcement layer within the concrete of the beam.

The angle of dispersion (θ_disp) cone is by default 45 degrees. When the default angle is not available then the angle should be adapted to the dimension of the cross-section with respect to values δ₂ and δ₃ (see Fig. 26).

The default value of the dispersion cone angle is 45 degrees, and it can be set in the concrete setup dialogue.

Fig. 22 Concrete setup for dispersion cone

b) Position of points A and B

The value of the length of the strut (L_strut) depends on the position of the points A and B (see Fig. 26). The points mean the following:

Point A – the end of the straight part of the bar after deducting the tolerances

Point B – corresponds to the starting point for balancing the internal forces in the support – i.e. located exactly above the edge of the effective supporting area.

The length of the strut (L_strut) will be calculated according to the following formulas

Direct wet/dry support

L_strut = a_1d

Fig. 23 Length of strut (L_strut) for direct support

Non direct support

L_strut = a_1d + 2*L_disp

Where

L_disp - length of the dispersion cone

Fig. 24 Length of strut (L_strut) for non direct support,

Splitting of reinforcement layers

The reinforcement is split to layers for the anchorage check. There are several rules for considering a layer as a part of a single layer. Only the reinforcement satisfying the following rules is considered as a part of a single layer:

• the same material and
• the same length and
• the same shape and
• located on the same level

For instance, when bars of a different length are located on the same level, they will be treated as 2 separate layers. The bars with the shortest available length should be used first.

Fig. 25 Example of splitting reinforcement layers

SaT calculation method

The procedure of the SaT analysis is described in the following figure. The calculation is made in three steps:

Check of the existing layer

• Check of longitudinal reinforcement
• Check of shear reinforcement

Design required area of

• Longitudinal soft reinforcement (see 4.3.1)
• Shear reinforcement (see 4.3.2)

Performing check with the new reinforcement again

• The procedure of the calculation of each value in the appropriate direction is clear from the following figure.

Fig. 26 Values in their direction for Non-direct SBEZ

Calculation of concrete strut

Calculation of concrete strut is divided to two parts:

• Determination of concrete strut area – compression zone
• Calculation of concrete strut capacity

Calculation of compression zone

At the beginning the first layer of reinforcement (with shortest length) is taken into account as the first compression zone

F_s,max,tot (i) = ΣF_s,max (i), where i=1...N

A_c,strut = b * (Z_sup - Z_inf)

Calculation of concrete strut capacity– F_cd,max

For each concrete strut the maximum force according to the following formulas is calculated :

F_cd,max,i = A_c,strut,i* cos(θm)*σ_Rd,max – capacity in inclined direction

Where:

σ_Rd,max is the maximum stress in the concrete strut see 6.61 [1]

σ_Rd,max = k2 ν´ f_cd

The values k₁; k₂ and ν´ are defined in Concrete > ULS > General.

Fig. 27 Concrete setup for strength of concrete strut

Calculation of reinforcement tie with respect to anchorage zone of bars

The forces in bars (Fs) are calculated for each reinforcement bar in each layer. And the total value in the layer is the sum of all forces in the layer. Decreasing is performed only for soft reinforcement and for postensioned tendons. It is not done for pretensioned strands, because the section of detail is situated in the anchorage length and the stress from bending is equal to maximal stress of strands is this section.

Calculation value Fs in the i layer ,

Where:

N the number of bars or strands in i-th layer

Fs the force in strands and longitudinal reinforcement with respect to the anchorage length in ULS in the considered section (capacity of strands according to the position in the anchorage length)

F_s(i) = A_s σ_s

F_p(i) = A_p σ_p

Values σ_s, σ_p have to be taken as the capacity of the layer (or strands) calculated from the reduced stress-strain relationships according to the position of the section in the anchorage length.

On the other hand, it is necessary to take into account the effect of bending on the capacity of the reinforcement. Due to the definition of the actual span, the CSS considered at the edge of the support has a non-zero bending moment.

The response in the “green line section” will be calculated under ULS assumptions for the materials, and the stress caused by the flexure will be subtracted from the capacity of the layer (or strands) in the anchorage zone.

σ_p = σ_p,orig – σ_p,bend

σ_s,= σ_s,orig – σ_s,bend

Fig. 28 Concrete setup for decrease of capacity of longitudinal reinforcement due to the stress caused by bending

Where

σ_p (σ_s) – the total value of the capacity in the strand (bars) in the anchorage zone (f_pd, or f_yd)

σ_p,orig (σ_s,orig) – the capacity of the strand (bars) in the green line according to the position of the green line in the anchorage zone

σ_p,bend (σ_s,bend)– the stress in the strand (bars) from the acting bending moment and normal force in the green line section according to the selected combination;

Decreasing of the capacity of the longitudinal reinforcement by the bending stress can be set in

Concrete > ULS > Details > Longitudinal reinforcement.

Fig. 29 Concrete setup

Decision of ultimate capacity

The program calculates the ultimate capacity. It means which material fails. Calculation of the force in layer “after reduction” Fs,max:

Failure of concrete strut – the force in reinforcement is bigger than in the concrete strut

f_cd,max / cos(θ_m) < F_s — F_s,max = f_cd,max

The total height of the compression zone is used: Z_sup = Z_sup,max

Failure of tie – the force in reinforcement is lower than in the concrete strut

f_cd,max / cos(θ_m) > F_s — F_s,max = F_s

Calculation a new height of the compression zone.

Calculation of total values for all layers

The total value of the maximum forces in the concrete strut f_cd,maxtot is calculated as

The total value of the maximum forces F_s,max,tot in the layer is calculated as

The total value of the maximum forces F_sw,tot in the vertical direction (for stirrups) is calculated as

Fig. 30 Equilibrium of forces

Performed check

Two checks are performed.

Check of equation F_sw,tot < V_ed and all reinforcement layers (compression zones) are not used

The values F_sw,tot < V_ed are compared and all layers are not used

If YES — check the next reinforcement layer

If NO — perform the next check

Check equation F_sw,tot ≥ V_ed

The values F_sw,tot ≥ V_ed are compared

If NO and all reinforcement layers (compression zones) are used — NOT OK — it is necessary to design additional reinforcement - 4.3.1

If YES — OK – calculation is finished

Calculate Check value <1,0

V_ed / F_sw,tot

Output of anchorage check results

The output tables are printed according to the used number of reinforcement layers (struts) in the anchorage check. The following values are printed:

a) Global check of longitudinal reinforcement – check of longitudinal reinforcement

b) Detailed check of longitudinal reinforcement – check of longitudinal reinforcement in each layer

The following values are available in Table composer δ₂, δ₃, a_1d, Z_sup, Z_inf, A_s(A_p) σ_s,tot(σ_p,tot)σ_p, σ_p,bend, σ_Rd,max, θ, θ_m;

Design of additional reinforcement in detail

Design of additional reinforcement is performed if it is required by the user, if it is specified in the concrete setup. The program can design:

• Additional longitudinal reinforcement - bars
• Additional shear reinforcement - stirrups

Design of additional longitudinal reinforcement

Design of additional longitudinal reinforcement can be split to the following parts:

• Design to the existing layer
• Design between the existing layers
• Design above the existing layers

The parameters (Concrete cover and Diameter) of the design reinforcement are taken from Concrete setup > Design defaults > Beams > Longitudinal reinforcement > Lower.

Fig. 31 Parameters for design of additional longitudinal reinforcement

Calculation of area of design additional reinforcement

The calculation of additional longitudinal reinforcement is an iterative solution. The first step is to insert one bar of the default design reinforcement and perform the whole check again. If still not ok, then it is needed to increase the number of bars in this new layer and perform the check again.

The area of the design additional soft reinforcement can be estimated according to this formula:

After the design of additional longitudinal reinforcement the calculation procedure is performed again.

Position of additional designed layer

The ratio and reserve are calculated for each layer. The program is searching the zone where Ratio = 1 and Reserve > 0. Where Ratio = F_s,max / F_s; Reserve = (f_cd,max – F_s,max) / f_cd,max

Start searching from the lowest compression zone upwards and design to this area an additional soft reinforcement.

This step is not possible for prestressed layer.

Fig. 32 Design additional reinforcement in nonprestressed cross-section

Fig. 33 Design additional reinforcement in prestressed cross-section

Concrete setup

There are several new options related to the design of additional longitudinal reinforcement in the concrete setup. These settings are situated in Concrete > ULS > Details > Anchorage check:

Fig. 34 Concrete setup for design of additional longitudinal reinforcement

Explanation of values from setup:

Design additional longitudinal reinforcement – If YES, then the design is performed

Reserve bigger than – the existing layer can be used only in case the reserve is bigger than this percentage

Anchorage detailing provision

Type of provision – type of designed longitudinal reinforcement

• Straight
• Bent

Vertical part – active only for type of provision – Bent; the length of bent; it is measured from the horizontal straight part to the top end of the vertical part

Fig. 35 Vertical part of additional reinforcement

Minimal horizontal straight length by user – YES/NO – if yes then the horizontal straight part will be the minimum of the user defined value

Minimal horizontal straight length value – the user defined minimum horizontal straight part

Final length as multiple of – YES/NO – if yes then the final length of the bar will be a multiple of the user defined value

Multiple of final length – the value which is used for rounding up

The length of additional longitudinal reinforcement, output table

The required additional longitudinal reinforcement has the following parameters. The minimum length (L_{straight, horizontal}) of anchorage bars should be measured from the green line. The output is performed for each reinforcement layer (strut).

Value L_bd (anchorage length of longitudinal reinforcement) is not calculated automatically in SCIA Engineer. For the time being the minimum length of lb,min is taken into account max(10Ø;100 mm) – formula 8.6 from EN 1992-1-1.

The default diameters and material of the longitudinal reinforcement are taken from the concrete setup or from the concrete member data if it is defined.

Fig. 36 Minimal recommended length for direct dry or wet

Fig. 37 Minimal recommended length for non-direct support

The final length of the additional longitudinal reinforcement depends on the setting in the concrete setup. There are two possibilities the shape of the additional longitudinal reinforcement (see Fig. 36):

• Straight
• Bent

When the user selects the Bent shape of additional longitudinal reinforcement then the following additional values are calculated:

Mandrel diameter - then mandrel diameter is determined according to the setting in Concrete setup > Detailing provisions > Minimum mandrel diameter bends hooks and loops

Fig. 38 Concrete setup for determination of mandrel diameter

The following table describes each calculated value and it is also a procedure for calculation of the length of additional longitudinal reinforcement. The final length of the reinforcement is determined as a multiple of the user defined value, the default value is 50 mm. The final length of all additional reinforcement is the longest length from them.

Fig. 39 Length of additional longitudinal reinforcement – direct dry/wet

Fig. 40 Length of additional longitudinal reinforcement – non-direct

Output table will be following:

Fig. 41 Output of additional reinforcement

Design of additional stirrups in end beam zone

This chapter is about the design of additional stirrups in the end beam zone due to anchorage of longitudinal reinforcement.

The stability scheme in Fig. 44 is based on a uniform distribution of stirrups along the strut corresponding to each reinforcement layer.

In order to satisfy this condition, the stirrups corresponding to the loads balanced by the layer i must be distributed between the position 0 and xi. The same applies to next layers. Hence the interval [0; xi] includes the stirrups corresponding to the layer i as well as a part of stirrups from layers n of lower ranking, with a ratio :

Fig. 42 Stability scheme with several anchorage reinforcement layers for direct dry/wet

The variable angle θ_s is used different for each layer and it is calculated from the geometry of the end beam zone according to following formula

Determination of value z for each layer

The verification of stirrups will be performed for each concrete strut. The distribution of stirrups must be checked for consistency against anchorage reinforcement.

For each compression zone and associated strut, the spacing of stirrups (defined during a regular beam design) should be checked and possibly adapted against the detailing of end-of-beam. The stirrups that are anchored in each strut must be checked with the corresponding lever arm z_i = d_i -0,1 h.

Fig. 43 Effective depth for each layer

Performing check of stirrups

For each i-th reinforcement layer the required area of shear reinforcement Ass,i is calculated from the longitudinal force in each layer Fst,max,i, which is obtain from the chapter 4.2.3

Where

Value θ_db,i = 0 for the temporary solution

Value A_ss,i is the area of stirrups from i^th layer along the distance 0x_i

Value a_ss,i is the area of stirrups from i^th layer per 1meter.

Where

Fig. 44 Distribution of stirrups in the anchorage zone

The values in the table are sorted according to the distance of the zones on the beam (e.g. 0x₃; x₃x₂; x₂x₁) and the value on the distance.

Distance of the stirrups s_ss,i will be calculated from required area of shear reinforcement a_ss,I for the area of one stirrups A_ss1 respecting the number of cuts.

The default diameter (d_ss), number of cuts (nss) and material of the stirrups are taken from the concrete setup or from the concrete member data if it is defined (see Project data and Concrete Advanced > Design defaults > Beams > Stirrups).

Fig. 45 Parameters of required shear reinforcement

The output is performed for each reinforcement layer (strut) and gives the total required area along the end zone. The maximum check value is presented to the user as the extreme.

The check is performed following Check value = a_ss,real / a_ss,req in each zone.

If a_ss,real / a_ss,req ≤ 1,0 — OK

If a_ss,real / a_ss,req > 1,0 — NOT OK; “The additional shear reinforcement have to be added according to required area.”

Table composer: x_i; θ ;d_i, h;

Check of details

This service provides the check of all details and gives the global results for all details. The service is situated below the SBEZ data in the concrete tree.

Fig. 46 Concrete tree

Service “Check of details” is used for calculation of “Check value” for all the defined details in the structure. Only ULS combination or classes are offered to the user in the properties. The properties of this service are.

Fig. 47 Property of service check details

Three action buttons are at the bottom of the property dialog:

• Refresh – this button starts the check of all details
• Concrete setup – this is a link to the standard Concrete setup and makes it possible to set the values related to the check of details
• Preview – by this button the calculated results are displayed in a table

The output table is following:

Fig. 48 Check of detail table

Document

The document is divided to several parts by different types of OTX file. There are the following OTX files:

• Bearing checks – all checks related to the Check of bearing areas
• Default – summary of all partial checks in the selected detail; overall check value
• Longitudinal reinforcement – all values related to the check of longitudinal reinforcement
• Parameters of detail – only the property table of a detail, in this OTX it is possible to change parameters of the detail through the document
• Shear reinforcement – all values related to the check of shear reinforcement

Fig. 49 Type of OTX in the document

Fig. 50 Default OTX

Fig. 51 Bearing check OTX

Fig. 52 Longitudinal reinforcement OTX

Fig. 53 Parameters of details

Fig. 54 Shear reinforcement

Restrictions and limitations

There are also some restrictions and limitations for the discussed checks. The user should take into account the following when using this functionality.

• Only the type of detail Standard beam end zone is possible.
• Only frame XYZ and XZ can be used.
• There is no possibility to use material Neoprene, Masonry and Mortar as interface material or material of supporting member.
• Only reaction with an upward direction is taken into account for both the check of bearing areas and SaT analysis.
• The structure has to be modelled as a real structure (with overhangs of beams in the support zone) , no axial scheme is supported in this calculation.

Examples

The theory described above was tested on the following three examples. The results are compared with manual calculations.

Direct dry - prestressed beam with one reinforcement layer

Used CSS with reinforcement layers - Y1770S7-9,3

Overview of the structure

Parameters of detail

Results

Check of bearing areas

• SCIA Engineer output

• Manual calculation output

Check of Longitudinal reinforcement

• SCIA Engineer output

• Manual calculation output

Check of shear reinforcement

• SCIA Engineer output

• Manual calculation output

Direct wet - nonprestressed beam with two reinforcement layer

Used CSS with reinforcement layers - Ø20 B600C

Overview of the structure

Parameters of detail

Results

Check of bearing areas

• SCIA Engineer output

• Manual calculation output

Check of Longitudinal reinforcement

• SCIA Engineer output

• Manual calculation output

Check of shear reinforcement

• SCIA Engineer output

• Manual calculation output

Non-direct - prestressed beam with two reinforcement layer

Used CSS with reinforcement layers - Y1770S7-9,3

Overview of the structure

Parameters of detail

Results

Check of bearing areas

• SCIA Engineer output

• Manual calculation output

Check of Longitudinal reinforcement

• SCIA Engineer output

• Manual calculation output

Check of shear reinforcement

• SCIA Engineer output

• Manual calculation output

Abbreviations

The following abbreviations are used in the document.

BSP	Beam strands pattern
CMD	Concrete member data
CSS	Cross-section
CZ	Compression zone
SaT	Strut-and-Tie analysis
SBEZ	Standard beam end zone
SEN	SCIA Engineer

Bibliography

[1] EN 1992-1-1 Eurocode 2, Design of Concrete Structures – Part 1: General rules and rules for buildings, European Committee for Standardization, December 2004.

[2] NF P 19-202-3 Norme francaise, DTU 23.3 P3, juillet 2006

[3] Navrátil, J., Prestressed concrete structures, Akademické nakladatelství CERM, 2006

[4] KP1 New beam system, Synthesis for anchorage and additional bars