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timber design to Eurocode 5. (IS EN ) rules including strength capacity tables for structural elements. James Harrington1, Malcolm. Structural timber design to Eurocode 5 / Jack Porteous & Abdy Kermani. p. ; cm. Includes bibliographical references and index. ISBN Eurocode 5: Design of timber structures - Part General -. Common rules and rules for buildings. Eurocode 5: Conception et calcul des structures en bois.
The truss is considered as a two dimensional frame structure, and the stiffness of the connections is adjusted according to the selected degree of stiffness. The natural frequencies of the roof trusses are computed from a dynamic analysis. The loads are evaluated according to Eurocode 0 and 1. All the load combinations are taken into account. Automatic generation of truss drawings. Detailed drawing of the truss structure and the connections are automatically produced. A specialised CAD modulus is included to customise, preview and print the drawings.
All the load combinations are taken into account. Automatic generation of truss drawings. Detailed drawing of the truss structure and the connections are automatically produced. A specialised CAD modulus is included to customise, preview and print the drawings. Dimensions You specify the main roof dimensions length, high or pitch. You can choose to specify dimensions at nodal points or at element ends. Cross section sizes are chosen from the various tables included in the program.
Tables with section sizes from different European countries are included in the program, and you can also specify you own. End cantilevers can be added on the sides. Supports at various nodes can be selected. Kirjapaino Markprint oy. Handbook of Finnish Plywood. Performance of structural insulated panels. Actions on structures. The content of this book relates to the design of timber and wood-related products for buildings in accordance with the requirements of EN The documents are structured on a hierarchical basis.
The latter approach provides a more realistic representation of the overall behaviour of the structure and is the philosophy that has been adopted for the Eurocode design suite. As stated in Chapter 1. EN covers the requirements for strength. It comprises three parts: Eurocode — Basis of structural design.
The Eurocode for the design of timber structures is EN These documents are sup- ported by a number of Eurocodes detailing the particular methods of design to be followed for the structural materials being used. Eurocode 5: Design of timber structures. In EN a limit states design philosophy in which the requirements concerning structural reliability are related to limit states.
A Principle is a statement or requirement that must be fully complied with unless an alternative is given in the document and an Application rule is a rule that will satisfy the Principle.
Alternative design rules can be used by the designer provided it can be demonstrated that these will fully comply with the Principles and will produce an alternative design equivalent in regard to serviceability.
For application in the United Kingdom. The BSI publications of the following Eurocodes are regularly referenced in the book and the abbreviation used in the text for the relevant document is as follows: General Actions — EC1 Densities.
Where an item in a Eurocode is prefixed by a number in brackets followed by the letter P it is a Principle and where it is only prefixed by a number in brackets it is an Application rule. If not included in the National Annex. This information is given in a National Annex. An important point to note. This has been included for in the book. Design of timber structures — Part General — Common rules and rules for buildings . Where it is considered that a national choice is appropriate for certain design rules or values of functions in a Eurocode.
In this section. A design requirement for a SLS. This is the ability of a structure or structural element to fulfil its design re- quirements over the design working life and is normally expressed in probabilistic terms. States beyond which the structure will not comply with the design requirements that have been set. This is the capacity of a structural element to withstand actions without failing. Effect of action.
This is the withstand capacity of the material at a failure condition. This is the term used for the internal stress resultants or displacements in the structure arising from the effect of the action. Limit states beyond which defined service criteria will not be met. Limit states. Ultimate limit states ULS. Limit states associated with collapse or equivalent forms of failure. This is the term used for an action that is not monotonic and can vary with time.
Reversible SLS. Permanent action. This is the term used for an action that will always act in the same direction i. Serviceability criterion.
Irreversible SLS. This is the term used for a load or force applied to the structure i. This term is also used for imposed displacements.
Variable action. Serviceability limit states SLS. For those facilities that come within the CC2 consequence category.
For a year reference period. Consequences classes. The adequacy of the design for structural resistance. RC2 and RC3 respectively. It should also be noted that achievement of the above reliability levels will depend on the checking standard used for drawings. Each consequence class is linked to a reliability class RC. The consequence category for most facilities in which timber or timber-related materials are used for structure or structural elements will be CC2. Annex B. It is to be noted that the design working life may or may not coincide with the reference period used to determine the design values for environmental factors.
Table 2. Where necessary or beneficial. The particular factors highlighted in EC0. Table B4. When dealing with timber structures. The indicative design working life of this category is 50 years. Provided the client implements a sound maintenance inspection policy and properly undertakes the maintenance requirements of the building and structure. In EC0. The design intent has to be defined at the outset. Where possible a robust structural system should be used. It is possible to establish limit states to define limits of satisfaction for numerous issues.
General EC0. This is particularly relevant to timber structures. Unless such a system is operated. The strength properties of timber and wood product structures are affected by changes in environmental conditions and it is essential that during the working life they function under the service class conditions for which they have been designed.
Where preservative treatments are used and they are critical in achieving the durability requirement. The fabrication and assem- bly must be fully in accordance with the specification requirements. It is advisable to consider the use of materials that will enhance durability. The limit state being the state beyond which the structure will no longer satisfy the design criteria and will be classed as unsatisfactory.
A maintenance strategy should be prepared at the outset of the design process and the building designed such that the structure can be accessed to allow the strategy to be implemented during the design working life. ISO . With regard to the other design situations. Transient design situations: Accidental design situations: Specific attention is drawn to the following ULS that are relevant to timber structures and must be considered: For normal structures there will be no requirement to design for seismic conditions in the United Kingdom and this design situation is not addressed in the book.
Persistent design situations: For the ULS one is dealing with extreme safety conditions and for the SLS it is the level of comfort and appearance that is being addressed and. The SLS should be agreed at the outset of the project and a distinction made between those states that will be irreversible and those that will be reversible.
Also protection of the contents supported by the structure can be included for in these states provided this requirement is agreed with the designer. The action combinations referred to above are discussed in EC0. The combinations of actions associated with these types of SLS are as follows: In such instances. Although it is possible to use probabilistic methods of analysis for verification.
In the reversible condition. Such conditions are treated in the same manner as those for ULS. The criteria used for the verification of the SLS should be associated with the following matters: EC0 has been structured to accommodate the following three types of SLS: It is stated in EC5. EC0 states that the characteristic value is based on the probability of 0. Characteristic values for self-weight. On this basis the return period will be 50 years.
It should also be noted that where a building carries more than one floor. When dealing with climatic actions e. Characteristic values Permanent actions G k Where this relates to the self-weight of the material. This criterion also applies to imposed loading on the floors of buildings. The characteristic value should. Variable actions Q k The characteristic values of the variable actions referred to in Eurocode EN These are the actions that do not remain monotonic and may vary with time.
These are the actions that remain monotonic and will vary by a negligible amount with time. Accidental actions Ad Because of the lack of statistical data relating to this condition.
These are as follows: For floor loading on buildings. For buildings. This is performed on the geometry of the deformed structure Figure 2. Characteristic values of the properties of timber and some of the commonly used wood-related products in timber design are given in Chapter 1. This is performed on the geometry of the deformed structure.
When analysing a structure. The exception to this rule is when stiffness-related functions are used in the derivation of a strength property.
This is performed on the initially defined geometry of the structure. The 5th-percentile value will apply to strength-related properties and the mean value will normally be used for stiffness- related properties. When dealing with timber or wood-related properties the characteristic value will be either the 5th-percentile value or the mean value.
It is the basis of most first-order linear elastic analysis computer programs Figure 2. The following descriptions are commonly associated with non-linear analyses incor- porating plastic behaviour: Section 5.
Because of the brittle nature of timber under tension-induced stress configurations. Alternative stress—strain relationships commonly used in non-linear analysis.
The effects of deviation from straightness of members have to be taken into account and this will be achieved by validation of the element strength using the design rules in EC5. As this is not a Principle in EC5. When designing joints formed with metal dowel type fasteners the strength equations in EC5 assume that failure at the joint will be in accordance with the principles of plastic theory.
Verification is undertaken at the relevant state to demonstrate that Efd is less than or equal to the design resistance Rd. Although all timber connections will exhibit semi-rigid behaviour to varying degrees. This is one of the apparent anomalies between modelling to determine the action effect i. In such situations. Rigid plastic behaviour. EC5 states that the connections may be considered to be rigid and. In this method. Based on the content of EC0.
Fk is the characteristic value of the action. For the design of timber and wood product structures in accordance with EC5. Frep is the value to be taken into account in the relevant combination of actions. It can be the main representative value i. In order to establish a common basis for design. The modification factor is extremely important in timber design and a brief overview of how load duration and moisture content effects are taken into account is given in the following sub-sections. Factors covering scale and volume effects are considered separately in EC5 and are discussed in 2.
In EC5. The effect of moisture content on the compressive strength of Douglas fir when loaded parallel to the grain. To take this effect into account in design.
A typical relationship between strength adjustment and moisture content derived from tests is shown for Douglas fir in Figure 2. When the moisture content is low. With timber. These factors are referred to in Table 2. The level of service class to be used in the United Kingdom for the type of element to be constructed is given in NA. Values for kmod based on the load duration referred to in 2.
This corresponds to climatic conditions leading to higher moisture contents than service class 2. Table 3. A summary of the values to be used to derive the design value at the ULS.
The highest values of timber strength will be obtained when structures function in service class 1 conditions and the lowest when they function in service class 3 conditions. Board type: With timber and wood-related products the value is dependent on the design state being considered.
This is taken into account by the application of modification factors and a summary of the factors referred to in EC5 that are most likely to arise in design. As above. When dealing with connections. Table 7. At the failure condition. The value of the member stiffness property to be used for other conditions will be different and the values to be used for the alternative situations that will arise in timber design are discussed in 2.
It also accounts for variation in material strength across the member section. For timber or wood product structures. To confirm that the elements of the structure will not fail under fatigue. To confirm that the structure and its elements will not fail under stress. Where displacements will affect the behaviour of the structure.
Where relevant. To confirm that the structure or any part of it is not unstable. To confirm that the foundations of the facility provide the strength and stiffness required by the structure.
Section Load combinations are applied at each relevant ULS and by the application of the partial factor method see 2. ULS a. The principal modification factors in EC5 are summarised in Table 2.
FRd is the design value of the corresponding resistance see 2. With accidental design situations. G k is the permanent action. For each relevant limit state the design value of the effect of actions must be derived.
To derive the combination of actions for persistent or transient design situations referred to in EC0 as the fundamental combinations and ignoring pre-stressing actions as they are not generally relevant to timber design. X d is the design value of the timber or wood product material property see 2. To achieve this. If the static equilibrium involves structural members. The examples given in the book are based on STR c.
OTE Table 2. For timber structures. The alternative use of the less favourable of equations 6. Adopting equation 6. Unless otherwise stated. To determine the load case producing the greatest design effect i. For the STR limit state. From calibration work undertaken by Gulvanes- sian and Holicky . Based on the content of Table NA. On this basis. For the example given in equations 2. Where there is a linear relationship between actions and effects.
It will be noted that equation 2. To determine the design value. If a reversible limit state condition has been accepted for the.
Using the symbols defined in 2. Although this option is not referred to in EC5. The United Kingdom. The design displacement. The Eurocode convention. Where the structure comprises members with different time-dependent properties. The final deformation is obtained by combining the instantaneous and the creep displacement.
Assuming all of the members. The traditional practice in the United Kingdom is to show the z—z axis as the longi- tudinal axis of a member and the x—x and y—y axes to denote the respective major and minor axes of its cross-section.
In the Eurocode suite the longitudinal axis is referred to as the x—x axis and the y—y and z—z axes are the respective major and minor axes of the cross-section. Member axes.
Where it is relevant to show the direction of the grain of the timber it is defined by the symbol used in Figure 2. Deformation is calculated in two different ways. For structures or members complying with the above conditions the final deformation. Values for the factor have been derived for timber and wood-based materials at defined environmental conditions when subjected to constant loading at the SLS over the design life. These deformations are shown diagrammatically in Figure 2.
The environmental conditions are referred to as service class 1. EC5 uses the characteristic combination of actions to derive the instantaneous deformation and the quasi-permanent load combination to derive the creep de- formation. Where an action is not permanent. EN  0. Assuming irreversible SLS conditions will apply. The factor is obtained from Table 3. For structures or members complying with the above conditions. The reduced stiffness properties are given in 2. When the strength of a connection is being considered and it comprises two timber elements.
For both situations. The instantaneous deformation is calculated as in 2. The application of the factor 2 to derive kdef values for connections may be inappro- priate for certain conditions and sizes of fixing. As the creep behaviour of the member is not relevant at this condition.
A connection comprising two timber elements with different time-dependent behaviour. In this situation. E mean E mean. For this condition. In accordance with the requirements of EC5. G mean. The design value of stiffness properties used in the analysis will therefore be E mean G mean K ser E d. This condition will apply where all members have the same time-dependent properties and the relevant stiffness related properties will be E mean.
G mean and K ser. Values for kdef for timber and some wood-related products are given in Table 2. G mean is the mean value of the shear modulus. This will be the case for structures where the members. E mean is the mean value of elasticity. K ser is the slip modulus. The final mean values are adjusted to the load component causing the largest stress in relation to strength and are as follows: For the final condition.
Where EC5 considers that plastic behaviour can be taken into account to enhance member strength. In the above equations. For connections. If this is a permanent action.
Con- sequently. After derivation of the stiffness-related properties in accordance with the above requirements. Although there has been considerable research and theoretical investigation into member size. If there are two members of differing volumes. Although not valid for some timber species. V1 and V2. Because timber and wood-related products are brittle materials. In this condition.
For timber sections. For bending stresses. Because the width of timber members does not vary significantly. The Weibull theory as it is commonly referred to has also been used to investigate volume effects as well as the effect of varying the types of loading configuration applied. The effects are not applicable to wood-based panel products. Factors have been included for bending and tensile strengths in solid timber.
For sizes greater than the reference size the factor is less than unity. Above the mm reference size kh is taken to be 1 and as the size of the beam decreases it follows the theoretical function until it reaches a maximum value of 1.
Relationships for the size effects used in EC5 for timber. No size factor is applicable for LVL when bent flatwise. The consequence of the above is that unlike designs in structural steel and reinforced concrete. EC5 has adopted a simplified approach and ignored certain of the effects. The characteristic strengths in bending and tension given in BS EN The tensile strength of LVL is also affected by the length of the member and the reference length used in EN For LVL.
As an example. To take these effects into account. The factor kh will apply to bending about the strong or the weak axis when dealing with solid timber but for horizontally laminated glued laminated timber. In such circumstances. In EC5 factor kh. The relationship is given in EC5. When sizes are less than the reference value the factor will be greater than unity. It takes advantage of the fact that stiffer members will take a greater share of the applied load than weaker members and that there will be a low probability that adjacent members in the system will have the same strength and stiffness characteristics.
The continuous load distribution system must be able to transfer the loads on the system from one member to the neighbouring members and for this condition ksys shall be taken to equal 1. This allows the member strength properties to be increased in value and is achieved by multiplying the relevant properties by a system strength factor.
This can be taken to apply where the load distribution system is as follows: The factor is only relevant where the system is able to redistribute load. The spacing of the trusses must not be greater than 1. EC5 factor kh for glulam beams in bending and tension compared with the theoretical value. In the apex zone of a double tapered. V0 NB: For length: For bending and tension and For the evaluation of kh laminated stress distribution: Figure 6.
In the apex zone of double tapered and curved beams: V In the apex zone of double tapered. Ed Design tensile reaction force at the end of shear wall i Fi. Ed Design axial force on a fastener Fax. Ed Design vertical load on wall i Fi. Rd Design load capacity per fastener in wall diaphragm Fi. Rd Design value of the axial withdrawal capacity of the fastener Fax. Latin upper case letters A Accidental action Ad Design value of an accidental action Af Cross-sectional area of a flange Aw Cross-sectional area of a web C A function of certain design properties of a material E Modulus of elasticity of a material E 0.
Values for the system strength factor for laminated floor plates made from solid timber or glued-laminated timber are given in EC5.
Rd Design racking resistance of panel i when using method A or wall i when using method B Fk Characteristic value of an action or force Frep Representative value of an action. If laminated timber flooring is to be used in the structure. Ed Design compressive reaction force at the end of shear wall i Fi. Rk Characteristic axial withdrawal capacity of the fastener Fc Compressive action or force Fd Design value of a force Fd.
Design moment M y. Ed Design value of a force in the x-direction Fy. Rk Characteristic load capacity of a connector along the grain Fv. Rk Characteristic load capacity per shear plane per fastener Fv. Ed Design shear force on web Fx. Ed Design shear force per shear plane of fastener. Ed Design value of a force in the y-direction G Permanent action G 0. Rd Design load capacity per shear plane per fastener. G Instantaneous deformation for a permanent action.
Q 1 u inst.
G Final deformation for a permanent action u fin. G u inst. Quality Management Systems. Structural Fire Design. General — Common Rules and Rules for Buildings. Basis of Structural Design. Requirements for Plywood for Use in Dry Conditions. General—Common Rules and Rules for Buildings. General Actions — Densities. Fundamentals and Vocab- ulary. Volume and stress distribution effects. Actions on Structures. Structural timber — variability and statistical modelling. Thelander- sson. Part 3: Requirements for Plywood for Use in Exterior Conditions.
Requirements for Plywood for Use in Humid Conditions.. Thomas Telford. ISSN British Standards Insti- tution.. Classification and Requirements. Proceedings of the I. Classification and Specifications. Self-Weight and Imposed Loads for Buildings.
UK National Annex to Eurocode 5: Mathcad can also be used to answer. Details are given at the end of the book. When expository text is added. It preserves the conventional symbolic form for subscribing. It is important to note that this chapter is not intended to teach Mathcad. It aims only to familiarise the readers with the Mathcad worksheet formats that are used to produce the design examples given in the book.
With a well-structured worksheet. Data can be presented in both tabular and graphical forms. While Mathcad employs the usual mathematical symbols i. The aim of this chapter is to demonstrate how the analysis and design calculations for structural timber can be incorporated into simple-to-use electronic notepads or worksheets using this software.
All of the design examples in the book are fully self-explanatory and well annotated. The aim is to encourage readers to use computing as a tool to increase their understanding of how design solutions vary in response to a change in one or more of the variables and how alternative design options can be readily obtained.
They have been produced in the form of worksheet files and are available on a CD to run under Mathcad 11 or higher. This will allow design engineers to arrive at the most suitable and economic solution quickly. They should not be seen as complete and comprehensive but rather as the foundations of a design system that can be developed further. The design worksheets given are intended as a source of study.
This is to illustrate the format and meaning of the operations used to produce the examples in this text. A simple calculation. With Mathcad. By defining variables and functions. The following sub-sections demonstrate how some simple operations are carried out in Mathcad. Mathcad computes and shows the result. Mathcad comes with multiple fonts and has the ability to print what you see on the screen through any Windows supported printer. The text box will grow as the text is entered. Now type.
Mathcad automatically performs unit conversions and flags up incorrect and inconsistent dimensional calculations. To obtain the result. Then type 10 in the empty placeholder to complete the definition for t. To begin typing text. Calculating with variables and functions. To enter another definition. Now that the variables acc and t are defined.
Mathcad will then create a text box in which you can type. Mathcad will show the colon as the definition symbol: Once the appropriate definitions are entered. To exit text mode simply click outside the text box. You can also define your own units if you so wish. The default unit for force times distance is joule and to display the answer in kN m. To illustrate the above. Mathcad will compute the result and also display the units of M as shown in Figure 3. The SI system is used and. Entering text.
The equation is structured to give the answer in N mm units providing the tensile strength of the bolt. The equation is My. To do this. Several of the equations given in EC5  are empirical and dimensionally incorrect. If the result is to be expressed in other units compliant with the SI system. The equation is then set up with the dimensions removed from each function.
When these functions have been defined within the calculation the minimum value. To obtain the solution. To obtain the answer. Equations using units.
The determination of the lateral torsional instability function. MathSoft Engineering and Education. To learn more about Mathcad.. British Standard Institution. Introduction to Mathcad for Scientists and Engineers. Small deflection bending theory is taken to apply and limitations on permissible deviations from straightness must comply with the criteria given in Section 10 of EC5. Flexural members have to satisfy the relevant design rules and requirements of EC5 .
This chapter deals in detail with the general requirements that are necessary for the design of flexural members made from straight solid timber or wood-based structural products of uniform cross-section in which the grain runs essentially parallel to the member lengths.
The equilibrium states and strength conditions i. Although the design principles used for the design of timber members in bending are essentially the same as those used for members constructed from other materials. Typi- cal examples are solid section rectangular beams. Other examples include glulam beams and composites thin webbed beams and thin flanged beams. Typical examples of timber beams. The design of tapered. Examples of flexural members. For strength-related conditions.
Although the determination of the critical load cases is not difficult. Where a load combination comprises actions having different load duration classes.
With the equilibrium related states the design effects will apply solely to matters associated with static instability. To be able to validate that the critical design effect of actions is being used. Where accidental situations have to be designed for.
The example covers the basic case of a simply supported beam subjected to permanent and variable actions. The loading conditions to be used for these states are defined in 2. For the serviceability limit states. For the examples given in the book.
In the case of the ultimate limit states. For the SLS. For the strength-related states. An indication of the work involved in determining the critical load cases that will result in the greatest design effects at the ULS and the SLS is given in Example 4.
For cases where the beam loading is high or longer span beams are being used. Beam span. For solid timber beams and joists as well as built-up flooring beams it is usually acceptable to assume an additional length of 50 mm to be added to the clear span.
Adopting the symbols defined in Chapter 2. In such instances the design span. The value of W y is dependent on the distance from the y—y axis and the values used in design for z are the distances to the extreme tension and compression fibre position on the section.
Cross-section of a rectangular beam. The procedure for determining the relative slenderness ratio for bending of a member about its strong axis is given in 4. This is achieved by compliance with equation 4. Lateral torsional instability affects a member bent about the y—y axis when the compression face of the member is not fully restrained against lateral movement and the relative slenderness for bending.
When a member is subjected to bending. The design procedure for members that are not affected by lateral torsional instability is addressed in 4. Where the relative slenderness for bending of a member about the y—y axis exceeds 0. For bending about this axis. Because the factor is dependent on the member size in the direction of bending. As the effect only applies to solid timber and LVL when bent flatwise. Strength information for timber and the commonly used wood-based structural products is given in Chapter 1.
Lateral torsional buckling of a beam subjected to uniform end moments M applied about the major axis lateral buckled position shown solid.
Sections in which the second moment of area about the y—y and z—z axes has the same value e. For a member with a design span. This mode of failure is termed lateral torsional buckling and is shown in section A—A in Figure 4. The bending moment at which elastic buckling will occur is termed the elastic critical moment and is a function of the nature of the loading on the beam.
Values for the factor are given in 6. When using a circular cross-section. Per cent overestimate in EC5 of the elastic critical moment of a rectangular beam when ignoring factor a.
For a rectangular section of breadth b. This is shown in Figure 4. In EC5 factor a is ignored for solid rectangular timber softwood beams and the elastic critical moment becomes: For all practical sizes of solid timber beam.
LVL or glued-laminated timber. For situations where different end fixing conditions exist and moment is induced by other types of loading. W y is the section modulus of the beam about the y—y axis. As it is extremely difficult to achieve full restraint against lateral rotation in plan at the ends of a single span beam. Equations 4. LVL or glued-laminated timber rectangular section beam subjected to a uniform moment at each end and will equate to the solution derived from equation 6.
With softwood rectangular sections. The effective length is obtained by adjusting the design span to take account of the effect of the change in loading and end fixing conditions and values for commonly used cases in timber design are given in Table 4. LVL or glued-laminated rectangular beams. When designing solid softwood rectangular beams. Beyond this limit. To link the buckling strength of a beam. If the load is applied at the compression face of the beam. EC5 Beam end condition: Equation 4.
For behaviour within the linear elastic range of the beam. The relationship in equation 4. For relative slenderness values between 0. The design rules in EC5 for strength validation are considered to take the effect of this imperfection into account. Where lateral instability effects can occur in beams.
The value of kcrit to be used is given in Table 4. By limiting the out of alignment in a beam to the maximum values given in EC5. A graphical representation of kcrit plotted against the relative slenderness ratio for bending.
In Table 4. The bending strength is derived from the characteristic bending strength in accor- dance with equation 4. For a strength class of timber. At intermediate values of relative slenderness ratio.
To demonstrate that lateral buckling of the beam will not occur. The effect of deviation from straightness is also relevant within this range of relative slenderness however the adoption of linear behaviour as defined in equation 4.
Lateral restraint can be provided by blocking or strutting the beam at positions along its length. Where the beam is supported laterally along the length of its compression flange. Examples of the provision of lateral support. The lateral restraint must provide adequate strength and stiffness to the beam and guidance on these requirements is given in Chapter 9. I is the second moment of area of the cross-section about the neutral axis. In accordance with elastic bending theory. Notch subjected to bending.
S is the first moment of the area above the shear stress level about the neutral axis. V is the shear force at the position being considered. The value of the shear stress at any level in the cross-section of a beam.
See Examples 4. Where a beam has a rectangular cross-section. For members having a notch and subjected to bending. In the proposed draft amendment summarised in Appendix C. Shear stress components in a member: When deriving the shear strength of members subjected to bending. LVL glulam and wood-based products on shear resistance.
V a A shear component parallel to the b Both shear components perpendicular grain to the grain rolling shear situation Fig.