Linear and Planar Elements Conventions

 

This page explains the commonly used shortcuts and conventions graphically for planar and linear elements, offering clarity on how these elements are defined, interact, and behave within the software environment. 

 

 

Linear and planar elements conventions

Discover below more about the linear and planar elements conventions:

 

  1. Linear elements conventions

Forces

Local axes

Local axes:

  • in red: local x

  • in green: local y

  • in blue: local z

Normal force

Fx: Normal force

Attention! Fx is positive in case of tension and negative in case of compression, regardless of the orientation of local x.

Shear force

Fz: shear force due to a load applied along the local z axis

Shear force

Fy: shear force due to a load applied along the local y axis

Bending moment

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)

Bending moment

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

Linear 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)

Linear reinforcement

Ay: reinforcement provided by moment Mz

Shear reinforcement

Atz: shear reinforcement provided by the shear force Fz

Shear reinforcement

Aty: shear reinforcement provided by the shear force Fy

 

Stresses

Stresses in Advance Design

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)

 

 

 

  1. Planar elements conventions

Forces

Planar forces in Advance Design

Local axes:

  • in red: local x

  • in green: local y

  • in blue: local z

Planar forces in Advance Design

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)

Shear force

Fxz: shear force in the plan of the x normal, in the direction parallel to z

Shear force

Fyz: shear force in the plan of the y normal, in the direction parallel to z

Bending moment

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)

Bending moment

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

Reinforcement bars

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).

Reinforcement bars

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

Planar stress in Advance Design

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)

 

 

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