This calculator is for determining the moment and shear capacities of a steel plate which is acting as a beam and bending about its minor axis. It is not suitable for plates bending about their major axis, as these are subjected to additional checks related to their section classification. This tool also acts as a plate steel weight calculator, determining the weight of the plate in kg/m.

The user will need to input:

• The width and thickness of the plate.
• The grade or alternatively, a custom yield strength of the plate.
• Design bending moment and shear force exerted on the plate.
• The analysis method for determining the bending moment capacity.

Using these values, the calculator will determine the bending and shear capacity of the plate and compare these capacities to the applied actions to return a utilisation ratio for the plate.

The plate bending design is defined by Section 6 of EN 1993-1-1. The capacity is compared to the applied design force as laid out in equation 6.12:

M_Ed / M_c,Rd ≤ 1.0

M_c,Rd is the design moment capacity and can be calculated by multiplying the section modulus by the steel yield strength, divided by the partial factor for the resistance of cross-sections (γ_M0 = 1.0):

M_c,Rd = W * f_y / γ_M0

Where W is the plastic or elastic modulus depending on the classification of the section (see Elastic vs Plastic Capacity for further clarification on selection).

The plastic section modulus of a rectangle can be calculated as: W_pl = b * t² / 4

The elastic section modulus of a rectangle can be calculated as: W_el = b * t² / 6

The elastic capacity of a member assumes that the most extreme fibres of the cross-section reach the yield stress of the material, while the rest remains in the elastic range. In contrast, plastic analysis allows parts or the entirety of the cross-section to reach the yield stress, enabling the formation of plastic hinges and resulting in greater moment capacity.

Section 5.6 of EN 1993-1-1 defines the conditions under which plastic analysis may be applied.

EN 1993-1-1 uses cross-section classification to determine which analysis method is appropriate:

• Class 1 and 2 sections are suitable for plastic analysis, as they can develop and sustain a plastic hinge without local buckling.
• Class 3 and 4 sections are limited to elastic analysis, as they are susceptible to local buckling before full plastic resistance can be developed.

The plates assessed in this calculation fall outside the typical scope of section classification. However, based on their geometry and assumed behaviour, they are considered to meet the requirements for plastic design as defined in Section 5.6. Therefore, their bending and shear capacities are calculated using the same approach applied to Class 1 and 2 sections.

The plate shear design is defined by Section 6 of EN 1993-1-1. The capacity is compared to the applied design force as laid out in equation 6.17:

V_Ed / V_c,Rd ≤ 1.0

V_c,Rd is the design shear resistance and can be determined using equation 6.18 for plastic analysis:

V_c,Rd = V_pl,Rd = A_v ( f_y / √3 ) / γ_M0

Or using equation 6.19 for elastic analysis:

V_c,Rd = V_el,Rd = τ_Ed / f_y / ( √3 · γ_M0 )

In order to calculate the shear capacity of a section using plastic analysis (equation 6.18), there are several criteria that need to be met:

• The cross-section is compact enough (typically Class 1, 2 or 3).
• The section is not susceptible to shear buckling (i.e. when the web isn't slender).
• The section is not subject to torsion (clause 6.2.6(2)).
• You are able to define a clear shear area, 𝐴𝑣.

As discussed in Elastic vs Plastic Moment Capacity, the plate in this calculation falls outside of the scope of section classification, so the first point is not applicable. The remaining three points above are applicable to and satisfied by plates designed in this calculator, hence only plastic shear is considered.

The yield strength of a steel section is dependent on its Grade, with higher grades having higher yield stresses. The yield strength of Hot Rolled and Fabricated sections vary depending on the thickness of the section. Thicker steel sections typically have lower yield strengths than thinner sections of the same Grade.

Table 3.1 in EN 1993-1-1 shows the yield and ultimate strengths for different typical steel grades. This calculator allows the user to select from the typical steel grades documented in EN 10025-2, but allows for a custom yield strength to be specified.

When considering a plate that is subject to high shear forces (over 50% of the shear capacity of the section), the bending capacity of the section is reduced. Section 6.2.8 addresses this phenomenon by reducing the yield strength of the section by a factor of (1 - ρ).

The weight of the plate is calculated by multiplying the width and thickness provided by the user with the density of steel, which is taken as 7850 kg/m³.

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