Chapter. Masonry Design

Transcription

1 Chapter Masonry Design The masonry design section contains modules for the analysis of reinforced masonry beams subjected to pure bending and unreinforced masonry walls subjected to axial compression and out of plane bending about two axes. Masonry Design 7-1

2 Quick Reference Masonry Design using PROKON 3 Masonry Section Design 4 Masonry Wall Design Masonry Design

3 Masonry Design using PROKON The masonry section design module, MasSec, is mainly used for the design of members such as lintels and masonry that span large openings in walls. MasWall, on the other hand is ideally suited for the design of wall panels and bearing walls. Code of practice support is currently limited to SABS Characteristic compression strengths for masonry units are calculated based on unit geometry, nominal strengths and tables in the abovementioned code of practice. All the masonry modules provide a detailed Calcsheet on design methodology and results, i.e. a complete record of the design is generated automatically. Current development includes support for reinforced masonry walls, columns and arches. Masonry Design using PROKON 7-3

4 Masonry Section Design The masonry section design module, MasSec, determines the resistance of a reinforced masonry section loaded in pure bending. The module is standalone, i.e. it does not post process results from any of the analysis modules. 7-4 Masonry Section Design

5 Theory and application A brief background is given below regarding the application of the design codes. Design scope The masonry section design module verifies the resistance of a reinforced masonry beam at a critical section. It is assumed that the loads imposed on the beam causes uniaxial bending and a shear force only. The following limitations apply: No direct support for composite action, e.g. masonry beam and prestressed a lintel. No support for doubly reinforced sections. Design codes The program designs masonry sections according to the following codes of practice: SABS Units of measurement MasSec supports both Metric and Imperial units. Symbols Where possible, the same symbols are used as in the codes of practice: Dimensions b : Section breadth (mm). d : Effective depth, i.e. distance from the compression face to the tension steel centroid (mm). z : Moment lever arm (mm). Masonry Section Design 7-5

6 Design results M r : Moment resistance (knm). M u : Applied ULS moment (knm). V r : Shear resistance (kn). V u : Applied ULS shear (kn). Design parameters Stresses a : Shear span (m), or unit correction factor (unitless). A s : Tension steel area (mm²). γ mm : Partial material safety factor for the masonry unit. γ ms : Partial material safety factor for the reinforcement. L max1,2 : Limiting lengths due to stability considerations (m). f y : Ultimate tensile strength of the tension steel (Mpa). f yy : Ultimate tensile strength of the shear steel (Mpa). f nom : Nominal compression strength of the masonry unit (MPa). f k : Characteristic compression strength of the masonry unit (MPa), i.e. the strength of the unit in a beam or wall, dependence on unit aspect ratio removed. f v : Shear stress due to V u (MPa). f v : Adjusted shear stress (MPa), modified based on the shear span. f br : Bond resistance (MPa). f bu : ULS bond stress due to V u (MPa). Design parameters Tension steel area As MasSec only verifies the resistance of a section, the diameter and number of bars are required parameters during the input stage. 7-6 Masonry Section Design

7 Physically, the tension reinforcement is usually either conventional bars, as used for concrete, or hard drawn wires. The conventional bars are used with special concrete block masonry units which have voids specifically intended for reinforcement. These voids are then filled with concrete after steel placement to form a solid, reinforced unit. Wires are placed in bedding joints, and as such, are suitable for use with standard format brickwork. Partial material safety factors The safety factors for masonry units have a fairly wide range, due to the wide range of materials and the measure of control during manufacturing and construction. See the applicable code of practice for details. Stresses Manufacturers usually quote a nominal compression strength for the masonry units that they provide. This nominal strength is derived from a simple crushing test. Due to the variability in masonry unit dimensions, this nominal strength cannot be used as the actual crushing strength of the unit. Values from crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter. This can be by testing a small, standard, wall panel to failure and using equations provided in the applicable code of practice to determine characteristic compression strength for the unit. Alternatively, most codes of practice also provide tables of characteristic strengths versus aspect ratio and nominal strengths. In MasSec, any one of the two approaches can be used. Masonry Section Design 7-7

8 Design of masonry beams The module consists of three pages or tabs: Input, which is further subdivided: o o General, for parameters concerning materials and masonry unit. Geometry and loads, for parameters concerning the beam and loading. Design, which displays a summary of the design results. Calcsheet, which provides fully annotated design documentation General input 7-8 Masonry Section Design

9 The masonry unit to be used in the beam is completely defined by the first table on this tab. The three available unit types and associated input parameters are tabulated below. Solid unit Hollow unit Hollow grouted unit *This parameter is only used for the graphical output. Width, Length, Height, Joint size Width, Length, Height, Joint size Shell thickness*, % solid material Width, Length, Height, Joint size Shell thickness*, % solid material Percentage solid material refers to the area perpendicular to the loading in the crushing test, usually this would be width x length. The percentage solid material would then be (total area void area) as a percentage of the total area. Masonry unit sizes are based on the modular concept, i.e. any dimension of the unit added to a joint thickness of 10mm yields a multiple of 100. The table below indicates the recommended nominal unit dimensions applicable to South Africa. Burnt clay Calcium silicate Concrete 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 190 x 190 mm 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 100 x 190 mm 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 190 x 190 mm Masonry Section Design 7-9

10 The second table on this tab contains the parameters pertaining to material strengths and reinforcement position. If the masonry units have been tested to failure as specified by the applicable code then f k can be entered directly in this table. If only nominal strengths are available, enter the nominal strength and MasSec will calculate f k. The table below lists the available nominal strengths available in South Africa. Burnt clay Calcium silicate Concrete 3.5 MPa 7 MPa 10.5 MPa 14 MPa 17 MPa 7 MPa 14 MPa 21 MPa 35 MPa 3.5 MPa 7 MPa 10.5 MPa 14 MPa 21 MPa Steel strength, positioning and type, as well as mortar class must be chosen in this table as well Masonry Section Design

11 Geometry and loads input The first table on this tab defines the type and geometry of the masonry beam. The following beam types are supported: Single leaf - Single leaf of masonry Collar jointed - Double leaf of masonry, where the small void between the two leaves of masonry is filled with mortar or concrete Grouted cavity - Double leaf of masonry, where the larger void between the two leaves is filled with concrete with strength of at least f k. The dimensions of the beam section, the clear span and the type of support are also chosen on this table. The second table provides parameters for the steel as well as a load distance parameter and a bearing length. The load distance is the distance of the critical section from the left hand support the resulting shear enhancement is allowed in certain cases. The last table requires the input of ULS loads on the critical section. Masonry Section Design 7-11

12 Design summary This tab provides a tabular and diagrammatic summary of the design. Two cases of bending failure are presented on the diagram and the minimum chosen as the section strength in bending: Compression failure Over-reinforced beam, masonry ruptures in compression before the steel yields. Tension failure Under-reinforced beam, steel yields before the masonry ruptures in compression. Other design checks are tabulated with action effect (loading) versus the resistance effect (strength). Steel required and provided is tabulated in the left bottom corner of the tab Masonry Section Design

13 Calcsheets The Calcsheet provides a fully annotated design document which can be printed or sent to the CalcPad for permanent storage. Display settings for the Calcsheet are controlled by the output settings button, on the left bottom corner of the tab. Note: The Calcsheet is not saved with the rest of the input when the file is saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet output, send it to the CalcPad where it can be edited and saved. Masonry Section Design 7-13

14 Masonry Wall Design The masonry wall design module, MasWall, determines the resistance of an unreinforced masonry wall axially loaded in its plane or loaded out of plane. The module is standalone, i.e. it does not post process results from any of the analysis modules Masonry Wall Design

15 Theory and application A brief background is given below regarding the application of the design codes. Design scope The masonry wall design module verifies the resistance of an unreinforced masonry wall, subjected to one of the following loads: In plane axial loading (Bearing walls) Out of plane loading, causing biaxial plate bending (Wall panels) The following limitations apply: Currently no support for combined loading, i.e. bending and compression. No support for reinforced walls. Design codes The program designs unreinforced masonry walls according to the following codes of practice: SABS Units of measurement MasSec supports both Metric and Imperial units. Symbols Where possible, the same symbols are used as in the codes of practice: Dimensions t : Wall thickness (mm). h : Wall height (mm) e x : Calculated or actual eccentricity (mm). Masonry Wall Design 7-15

16 Design results M r : Moment resistance (knm). M cr : Cracked moment resistance (knm). M u : Applied ULS moment (knm). C r : Axial resistance (kn/m). C u : Applied ULS axial force (kn/m). q lat : Lateral pressure resistance, assuming a three pin arch collapse mechanism. (kn/m²) Design parameters Stresses γ mm : Partial material safety factor for the masonry unit. R : Slenderness ratio Z : Section modulus (mm³) e a : Additional eccentricity due to slenderness (mm). e t : Total eccentricity (mm). e m : Design eccentricity (mm), maximum of e t and e x. β : Capacity reduction factor t eff : Effective wall thickness (mm) h eff : Effective wall thickness (mm) f nom : Nominal compression strength of the masonry unit (MPa). f k : Characteristic compression strength of the masonry unit (MPa), i.e. the strength of the unit in a beam or wall, dependence on unit aspect ratio removed. f kx perp : Flexural tensile strength perpendicular to the bedding joints (MPa). f kx par : Flexural tensile strength parallel to the bedding joints (MPa) Masonry Wall Design

17 Design parameters Eccentricities Actual load eccentricity is assumed to vary from e x at the top of the wall to zero at the bottom, subject to additional eccentricity due to slenderness effects. Partial material safety factors The safety factors for masonry units have a fairly wide range, due to the wide range of materials and the measure of control during manufacturing and construction. See the applicable code of practice for details. Stresses Manufacturers usually quote a nominal compression strength for the masonry units that they provide. This nominal strength is derived from a simple crushing test. Due to the variability in masonry unit dimensions, this nominal strength cannot be used as the actual crushing strength of the unit. Values from crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter. This can be by testing a small, standard, wall panel to failure and using equations provided in the applicable code of practice to determine characteristic compression strength for the unit. Alternatively, most codes of practice also provide tables of characteristic strengths versus aspect ratio and nominal strengths. In MasWall, any one of the two approaches can be used. Similarly flexural tensile resistances parallel and perpendicular to the bed joints can be specified or left to MasWall for calculation. Masonry Wall Design 7-17

18 Design of masonry walls The module consists of three pages or tabs: Input, which is further subdivided: o o o General, for parameters concerning materials and masonry unit, as well as wall design type. Wall geometry for parameters concerning the wall type and dimensions. Loading, which allows the entry of multiple load cases. Design, which displays a summary of the design results. Calcsheet, which provides fully annotated design documentation General input 7-18 Masonry Wall Design

19 The masonry unit to be used in the beam is completely defined by the first table on this tab. The three available unit types and associated input parameters are tabulated below. Solid unit Hollow unit Hollow grouted unit *This parameter is only used for the graphical output. Width, Length, Height, Joint size Width, Length, Height, Joint size Shell thickness*, % solid material Width, Length, Height, Joint size Shell thickness*, % solid material Percentage solid material refers to the area perpendicular to the loading in the crushing test, usually this would be width x length. The percentage solid material would then be (total area void area) as a percentage of the total area. Masonry unit sizes are based on the modular concept, i.e. any dimension of the unit added to a joint thickness of 10mm yields a multiple of 100. The table below indicates the recommended nominal unit dimensions applicable to South Africa. Burnt clay Calcium silicate Concrete 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 190 x 190 mm 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 100 x 190 mm 190 x 90 x 90 mm 290 x 90 x 90 mm 390 x 90 x 190 mm 390 x 190 x 190 mm Masonry Wall Design 7-19

20 The second table on this tab contains the parameters pertaining to material strengths. If the masonry units have been tested to failure as specified by the applicable code then f k can be entered directly in this table. If only nominal strengths are available, enter the nominal strength and MasWall will calculate f k. The table below lists the available nominal strengths available in South Africa. Burnt clay Calcium silicate Concrete 3.5 MPa 7 MPa 10.5 MPa 14 MPa 17 MPa 7 MPa 14 MPa 21 MPa 35 MPa 3.5 MPa 7 MPa 10.5 MPa 14 MPa 21 MPa Similarly values for flexural tensile resistances should be available in the applicable code of practice. The design type should be chosen on this tab: Vertical loads axially loaded bearing walls Lateral loads on panels design for biaxial plate bending The layout of subsequent tabs in the input process will vary according to the design type chosen Masonry Wall Design

21 Wall geometry input Vertical loads The table on this tab defines the type, geometry and stiffeners (if any) of the masonry wall. The following wall types are supported: Single leaf - Single leaf of masonry Collar jointed - Double leaf of masonry, where the small void between the two leaves of masonry is filled with mortar or concrete Cavity - Double leaf of masonry, with a void between the two leaves. Wall height, length and cavity size (if required) can be entered on this tab. Possible values for the horizontal restraint are: (Refer to SABS 0164 for details) Simple No rotational fixity at the top of the wall. Enhanced Partial rotational fixity at the top of the wall. Similar rotational fixities can be specified for the vertical edge(s) of the wall. Masonry Wall Design 7-21

22 MasWall also supports vertical stiffeners between the wall edges. These stiffeners can be either piers (small columns) or intersecting walls. Once vertical stiffeners have been selected, they need to be dimensioned as well. Wall geometry input Lateral loads on panels The table on this tab defines the type, geometry and edge restraint of the masonry wall panel. The following wall types are supported: Single leaf - Single leaf of masonry Collar jointed - Double leaf of masonry, where the small void between the two leaves of masonry is filled with mortar or concrete Cavity - Double leaf of masonry, with a void between the two leaves. Wall height, length and cavity size (if required) can be entered on this tab. Edge restraints can be specified for each edge individually as free, simple or fixed Masonry Wall Design

23 Loads input Vertical loading For this loading type, axial forces and eccentricity with respect to the wall centreline can be entered on this tab. Multiple load cases are supported. Note that all loads should be ULS loads. Masonry Wall Design 7-23

24 Loads input Lateral loads on panels For this loading type, moments parallel and perpendicular to the bedding joints can be entered directly. A dead load pressure on the level of moment parallel to the bedding joints is required to calculate the cracked moment resistance. Alternatively the moment calculator button can be used to calculate moments based on a lateral pressure. This calculation makes use of the moment tables in the code of practice which are in turn derived from yield line equations Masonry Wall Design

25 Design summary This tab provides a tabular and diagrammatic summary of the design. The two resistance moments are shown on the diagram. Other design checks are tabulated with action effect (loading) versus the resistance effect (strength). Masonry Wall Design 7-25

26 Calcsheets The Calcsheet provides a fully annotated design document which can be printed or sent to the CalcPad for permanent storage. Display settings for the Calcsheet are controlled by the output settings button, on the left bottom corner of the tab. Note: The Calcsheet is not saved with the rest of the input when the file is saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet output, send it to the CalcPad where it can be edited and saved Masonry Wall Design