# Conventions Common data

• NodeI: Number of 1st node element

• NodeJ: Number of 2nd node element

• NodeK: Number of 3rd node element

• NodeL: Number of 4th node element

• dofDX: Translation degree of freedom along the global X axis

• dofDY: Translation degree of freedom along the global Y axis

• dofDZ: Translation degree of freedom along the global Z axis

• dofRX: Rotation degree of freedom about the global X axis

• dofRY: Rotation degree of freedom about the global Y axis

• dofRZ: Rotation degree of freedom about the global Z axis

• LocRes: Location of result on element

• Material: Material of element

• Section1: Cross section of element at 1st end

• Section2: Cross section of element at 2nd end

• Connection1: Boundary conditions at 1st end

• Connection2: Boundary conditions at 2nd end

• Angle: Rotation angle about the element local axis (ø)

• Length: Length of line element

• Thickness: Element thickness at 1st joint

• Slopex: Slope along the local x axis

• Slopey: Slope along the local y axis

• Weight: Element weight

• CaseType: Type of load case (i.e., static, seismic, etc.)

• E: Young's modulus

• nu: Poisson's ratio

• W/V: Density

• Alpha: Coefficient of thermal expansion

• Sx: Cross sectional area effective in normal force

• Sy: Shear area in the y direction

• Sz: Shear area in the z direction

• Ix: Torsion constant

• Iy: Bending inertia about the local y axis

• Iz: Bending inertia about the local z axis

• Wx: Torsion modulus

• W1y: Bending modulus y for negative z

• W1z: Bending modulus y for positive z

• W2y: Bending modulus z for negative y

• W2z: Bending modulus z for positive y Common coordinates

• X: Element X coordinate

• Y: Element Y coordinate

• Z: Element Z coordinate

• XCenter: X coordinate at the element center

• YCenter: Y coordinate at the element center

• ZCenter: Z coordinate at the element center

• X1: X coordinate of element 1st end

• Y1: Y coordinate of element 1st end

• Z1: Z coordinate of element 1st end

• X2: X coordinate of element 2nd end

• Y2: Y coordinate of element 2nd end

• Z2: Z coordinate of element 2nd end Common displacements

• DX: Displacement along the global X axis

• DY: Displacement along the global Y axis

• DZ: Displacement along the global Z axis

• D: Global displacement

• RX: Rotation about the global X axis

• RY: Rotation about the global Y axis

• RZ: Rotation about the global Z axis

• Dx: Displacement along the local x axis

• Dy: Displacement along the local y axis

• Dz: Displacement along the local z axis

• d: Local displacement

• Lfy: Buckling length along the local y axis

• Lfz: Buckling length along the local z axis Common forces Support forces

• FX: Force along the global X axis

• FY: Force along the global Y axis

• FZ: Force along the global Z axis

• MX: Moment about the global X axis

• MY: Moment about the global Y axis

• MZ: Moment about the global Z axis Linear element forces

• Fx: Normal force along the local x axis

• Fy: Shear force along the local y axis

• Fz: Shear force along the local z axis

• Mx: Torsion moment about the local x axis

• My: Bending moment about the local y axis

• Mz: Bending moment about the local z axis Planar element forces

• Fxx: Normal force along the local x axis

• Fyy: Normal force along the local y axis

• Fxy: Shear force in the local xy plane

• Fxz: Transverse shear force

• Fyz: Transverse shear force

• Mxx: Bending moment about the local x axis

• Myy: Bending moment about the local y axis

• Mxy: Mixed bending moment

• F1: Maximum in plane force in the main directions

• F2: Minimum in plane force in the main directions

• AlphaF: Angle of F1 with the IJ direction

• M1: Maximum moment in the main directions

• M2: Minimum moment in the main directions

• AlphaM: Angle of M1 with the IJ direction Common stresses Support stresses

• SX: Support stress in the global X direction (ground stress)

• SY: Support stress in the global Y direction (ground stress)

• SZ: Support stress in the global Z direction (ground stress)

• S: Support stress in the global coordinate system (ground stress) Linear element stresses

• Sxx: Normal stress (due to all components)

• SxxMax: Maximum stress on element (due to all components)

• SxxMin: Minimum stress on element (due to all components)

• Sxy: Shear stress in the y direction (due to all components)

• SxyMax: Max envelope of the absolute value of the minimum shear stress in the y direction (due to all components)

• SxyMin: Min envelope of shear stress in the y direction (due to all components)

• Sxz: Shear stress in the z direction (due to all components)

• SxzMax: Max shear stress in the z direction (due to all components)

• SxzMin: Min shear stress in the z direction (due to all components)

• Sv: Von Mises stress (due to all components) Planar element stresses

• sxx_top: Normal stress in the local x direction (upper side)

• syy_top: Normal stress in the local y direction (upper side)

• sxy_top: Shear stress in the local xy plane in the y direction (upper side)

• sxz_top: Shear stress in the local xz plane in the z direction (upper side)

• syz_top: Shear stress in the local yz plane in the z direction (upper side)

• szz_top: Normal stress in the local z direction (upper side)

• sv_top: Von Mises stress (upper side)

• s1_top: Max stress in the main directions (upper side)

• alpha_top: Angle of s1 with the IJ direction (upper side)

• s2_top: Min stress in the main directions (upper side)

• sxx_mid: Normal stress in the local x direction (neutral plane)

• syy_mid: Normal stress in the local y direction (neutral plane)

• sxy_mid: Shear stress in the local xy plane (neutral plane)

• sxz_mid: Transverse shear stress in the local x direction (neutral plane)

• syz_mid: Transverse shear stress in the local y direction (neutral plane)

• szz_mid: Normal stress in the local z direction (neutral plane)

• sv_mid: Von Mises stress (neutral plane)

• Alpha_mid: Angle of s1 with the IJ direction (neutral plane)

• s2_mid: Min stress in the main directions (neutral plane)

• sxx_bot: Normal stress in the local x direction (lower side)

• syy_bot: Normal stress in the local y direction (lower side)

• sxy_bot: Shear stress in the local xy plane in the y direction (lower side)

• sxz_bot: Transverse shear stress in the local xz plane in the z direction (lower side)

• syz_bot: Transverse shear stress in the local yz plane in the z direction (lower side)

• szz_bot: Normal stress in the local z direction (lower side)

• sv_bot: Von Mises stress (lower side)

• s1_bot: Max stress in the main directions (lower side)

• Alpha_bot: Angle of s1 with the IJ direction (lower side)

• s2_bot: Min stress in the main directions (lower side) Envelopes

• Max ( ): Max envelope of a force, stress or displacement

• Min ( ): Min envelope of a force, stress or displacement

• Max ( | | ): Max envelope of the absolute value of a force, stress or displacement

• Min ( | | ): Min envelope of the absolute value of a force, stress or displacement Supports

• KTX: Translation stiffness in the X direction

• KTY: Translation stiffness in the Y direction

• KTZ: Translation stiffness in the Z direction

• KRX: Rotational stiffness in the X direction

• KRY: Rotational stiffness in the Y direction

• KRZ: Rotational stiffness in the Z direction

• TX: Support with X direction translational restraint

• TY: Support with Y direction translational restraint

• TZ: Support with Z direction translational restraint

• RX: Support with X direction rotational restraint

• RY: Support with Y direction rotational restraint

• RZ: Support with Z direction rotational restraint Accelerations

• AX: Acceleration in the global X direction

• AY: Acceleration in the global Y direction

• AZ: Acceleration in the global Z direction

• A: Global acceleration Loads

• FX: Force in the global X direction

• FY: Force in the global Y direction

• FZ: Force in the global Z direction

• MX: Moment about the global X axis

• MY: Moment about the global Y axis

• MZ: Moment about the global Z axis

• Coefficient1: Magnitude of load at 1st end

• Coefficient2: Magnitude of load at 2nd end

• Coefficient3: Magnitude of load at 3rd end Mass

• Mass: Mass ID

• MX: Mass in the global X direction

• MY: Mass in the global Y direction

• MZ: Mass in the global Z direction

• IX: Mass inertia in the global X direction

• IY: Mass inertia in the global Y direction

• IZ: Mass inertia in the global Z direction Self weight

• X: Self weight in the global X direction

• Y: Self weight in the global Y direction

• Z: Self weight in the global Z direction Thermal loads

• DeltaT: Variation between the set temperature and reference temperature (°C) Imposed displacements

• DX: Imposed translation displacement along the global X axis

• DY: Imposed translation displacement along the global Y axis

• DZ: Imposed translation displacement along the global Z axis

• RX: Imposed rotational displacement about the global X axis

• RY: Imposed rotational displacement about the global Y axis

• RZ: Imposed rotational displacement about the global Z axis Steel Results

• E: Elasticity longitudinal module

• G: Shearing module • : Poisson's coefficient

• : Material elasticity limit

• L: Beam real length

• h: Shape height

• Sx: Beam section

• Sy: Reduced cross section of shear force according to the y axis

• Sz: Reduced cross section of shear force according to the z axis

• lx: Torsional inertia moment of the beam

• ly: Bending inertia moment of the beam following the local y axis

• lz: Bending inertia moment of the beam following the local z axis

• y: Plastic adaptation coefficient for bending along y axis

• z: Plastic adaptation coefficient for bending along z axis

• Lfy: Beam buckling length in the local plan (x,y)

• Lfz: Beam buckling length in the local plan (x,z)

• Ld: Length of upper or lower lateral-torsional buckling

• iy: Gyration radius • iz: Gyration radius • y: Slenderness ratio along the local y axis • z: Slenderness ratio along the local z axis

• : Maximal slenderness ratio • x: Normal stress (negative for a compression)

• k: Critical stress of Euler

• y: Critical stress of Euler

• z: Critical stress of Euler • : Deviation coefficient from the critical state • y: Deviation coefficient from the critical state • z: Deviation coefficient from the critical state • AMz: Diagram area of the Mz moment

• AMy: Diagram area of the My moment

• Mzmax: Maximal moments (in absolute value) on the local z axis

• Mymax: Maximal moments (in absolute value) on the local y axis

• Mw: Extremity moment of the highest absolute value

• Me: Extremity moment of the lowest absolute value

• d: No lateral-torsional buckling stress

• D: Coefficient depending on the piece dimensions

• C: Coefficient depending on the longitudinal distribution of the loads

• B: Coefficient depending on the load application level

• k: Buckling coefficient in pure compression

• k1: Buckling coefficient in bending compression

• kfz: Buckling coefficient in bending following the local z axis

• kfy: Buckling coefficient in bending following the local y axis

• kd: Lateral-torsional buckling coefficient

• s: Security coefficient for the section strength

• E: Security coefficient for the element stability

• max: Maximum resultant stress in an element Reinforced Concrete Result

• Axi: lower reinforcement along the x axis

• Ayi: lower reinforcement along the y axis

• Axs: upper reinforcement along the x axis

• Ays: upper reinforcement along the y axis

• Ay: longitudinal upper and lower reinforcement area along the y axis

• Aby: reinforcement along the y- axis

• Ahy: reinforcement along the y+ axis

• Az: longitudinal upper and lower reinforcement area along the z axis

• Abz: reinforcement along the z- axis

• Ahz: reinforcement along the z+ axis

• Amin: minimum reinforcement area

• Aty: transverse reinforcement area along the y axis

• Atz : transverse reinforcement area along the z axis

• Al: longitudinal reinforcement area

• Atmin: minimum transverse reinforcement area

• Lfy: Buckling length along the local y axis

• Lfz: Buckling length along the local z axis

• RV: Theoretical reinforcement ratio by volume unit

• RL: Theoretical reinforcement ratio by length unit

• RS: Theoretical reinforcement ratio by surface unit Linear and planar elements conventions

Linear and Planar Elements Conventions

1.    Linear elements conventions

Forces Local axes: in red: local x in green: local y in blue: local z Fx: Normal force Attention! Fx is positive in case of tension and negative in case of compression, regardless of the orientation of local x. Fz: shear force due to a load applied along the local z axis Fy: shear force due to a load applied along the local y axis My: bending moment about the local y axis. ( = the moment generates a load applied along local z) Note: My > 0 => the upper fibre (z+) is tensioned (generally, on the supports) My < 0 => the lower fibre (z-) is tensioned (generally, on the span) Mz: bending moment about the local z axis. (= the moment generates a load applied along local y) Note: Mz > 0 => the upper fibre (y+) is tensioned Mz < 0 => the lower fibre (y-) is tensioned

Reinforcement Az: reinforcement provided by moment My Az is provided with a “ - ” sign when in lower fibre and with a “ + ” sign when in upper fibre My positive provides Az reinforcement in upper fibre (because the upper fibre is tensioned). (generally, on the supports) My negative provides Az reinforcement in lower fibre (because the lower fibre is tensioned). (generally, on the span) Ay: reinforcement provided by moment Mz Atz: shear reinforcement provided by the shear force Fz Aty: shear reinforcement provided by the shear force Fy

Stresses Normal stress (normal force and moments) Shear stresses σxz: stress in the plan of the x normal, in the direction parallel to z σxy: stress in the plan of the x normal, in the direction parallel to y Von Mises stresses (normal and shear stress) 2.    Planar elements conventions

Forces Local axes: in red: local x in green: local y in blue: local z Fxx: Normal force along the local x axis Fyy: Normal force along the local y axis   Attention! Fxx is positive in case of tension and negative in case of compression, regardless of the orientation of local x (Idem for Fyy) Fxz: shear force in the plan of the x normal, in the direction parallel to z Fyz: shear force in the plan of the y normal, in the direction parallel to z Mxx: bending moment about the local x axis Note: Mxx > 0 => the upper fibre (z+) is tensioned (generally, on the supports)       Mxx < 0 => the lower fibre (z-) is tensioned (generally, on the span) Myy: bending moment about the local y axis Note: Myy > 0 => the upper fibre (z+) is tensioned (generally, on the supports) Myy < 0 => the lower fibre (z-) is tensioned (generally, on the span)

Reinforcement Axi and Axs: reinforcement bars parallel to the local x axis (provided by the moment Myy) Myy positive provides Axs reinforcement (in upper fibre) (because the upper fibre is tensioned). Myy negative provides Axi reinforcement (in lower fibre) (because the lower fibre is tensioned). Ayi and Ays: reinforcement bars parallel to the local y axis (provided by the moment Mxx) Mxx positive provides Ays reinforcement (in upper fibre) (because the upper fibre is tensioned). Mxx negative provides Ayi reinforcement (in lower fibre) (because the lower fibre is tensioned).

Stresses Normal stress (normal force and moments) Along x Along y Shear stresses σxz : stress in the plan of the x normal, in the direction parallel to z σyz : stress in the plan of the y normal, in the direction parallel to z Von Mises stresses (normal and shear stress)  What is SxxMax and SxxMin on a linear element?