Base Plate Design for Axial Load and Moment
Base plate design for axial load and moment depends on the magnitude and direction of the applied loads. The calculation procedure changes depending on whether the connection is governed by compression, tensão, or a combination of axial load and bending moment. Calculations from one case cannot always be reused in another, so the first step is to identify which category your design falls into.
Guia de projeto AISC 1 (3Edição RD) is the main reference for designing base plates with moment loads. It includes all the equations and a step-by-step calculation procedure. Isso é feito para verificar as equações que são formadas a partir do ACI produces a calculation set for designing base plates subjected to moment loads, following the procedures outlined in AISC DG1.
Set 1: Combined Axial Compression and Bending (Momento Baixo)
When a base plate is loaded with moment, it may seem that the plate will tip to one side. Contudo, when the compression load is large, the eccentricity (the moment divided by the axial load) can remain within the critical eccentricity of the connection. Nesse caso, the applied load is resisted entirely by bearing on the concrete, and the anchors carry no uplift force. This is the most ideal case for base plate design, since the anchors act only as holding-down bolts.
How to Determine if the Base Plate Is in the Low-Moment Compression Case:
The first step is to calculate the eccentricity of the load. We do this by dividing the moment load, \(M_r\), by the axial load, \(P_r\).
\( e = \dfrac{M_r}{P_r} \) (AISC DG1 3rd Edition Eq. 4-39)
The next step is to determine the critical load eccentricity, \(\varepsilon\).
\( \varepsilon = \dfrac{N}{2} – \dfrac{Y}{2} \) (AISC DG1 3rd Edition Eq. 4-41)
To determine the critical load eccentricity, we need two dimensions. A \(N\) dimension is the width of the base plate, which is specified in the design. The second dimension is the \(Y\) dimensão, which represents the total bearing width. A \(Y\) dimension starts at the edge of the base plate and extends inward toward the center of the base plate. See the figure above for an illustration.
Em outras palavras, the location of the critical load eccentricity is measured from the center of the base plate to the midpoint of the \(Y\) dimensão. As the value of \(Y\) decreases, o valor de \(\varepsilon\) increases.
The low moment case controls when the actual eccentricity is less than or equal to the critical load eccentricity.
\( e \leq \varepsilon \)
Agora, we want to determine the value of \(Y\) dimensão, specifically the smallest dimension it can have. Note that the downward axial force \(P_r\) is equal to the bearing width \(Y_{min}\) multiplied by the bearing stress per unit length \(q_{max}\) .
\( P_r = Y_{min}q_{max} \)
Rearranging this equation gives:
\( Y_{min} = dfrac{P_r}{q_{max}} \) (AISC DG1 3rd Edition Eq. 4-36)
We then assume this bearing stress is applied over the full length of the base plate, \(B\). To obtain the maximum bearing stress per unit length, \(q_{max}\), we multiply the maximum allowable bearing capacity of the concrete, \( f_{p,max} \) to the base plate length, \(B\). Remember that we are maximizing the allowable bearing capacity of the connection in order to minimize \(Y_{min}\).
\( q_{max} =f_{p(max)} B \) (AISC DG1 3rd Edition Eq. 4-37)
The bearing capacity of the concrete is given by the equation below. An example of how to use this equation is provided in this SkyCiv Design Example. Feel free to check our the step-by-step procedure.
\( f_{p(max)} = 0.85 f’_{c} \sqrt{UMA_{2}/UMA_{1}} \leq 1.7 f’_{c} \) (AISC DG1 3rd Edition Eq. 4-2)
O termo \( f’_{c} \) is the compressive strength of the concrete. This is usually specified in the design. Common values are 3 ksi and 4 ksi. The areas A2 and A1 are the bearing area of the support (concreto) and the loaded bearing area (placa de base), respectivamente.
Em alguns casos, engineers may assume that the support area is equal to the loaded area \(UMA_{2} = A_{1}\) as this is also conservative. If the actual values are needed to increase capacity, an iterative procedure may be used to solve the exact A1 and A2 values. No Calculadora de placa base gratuita SkyCiv, this iteration is already implemented.
Finalmente, the critical eccentricity equation can be simplified to:
\( e_{crit} = dfrac{N}{2} – \dfrac{P_r}{2 q_{max}} \) (AISC DG1 3rd Edition Eq. 4-40)
Design checks needed for Low Moment Case (compressão + Dobra):
- Rolamento de concreto
- Base plate yielding at the bearing interface
Set 2: Combined Axial Compression/Tension and Bending (Grande momento)
If the eccentricity is larger than the critical eccentricity, that is the axial load is relatively small compared to the moment load, the base plate tends to tip over, with compression on one side and tension on the other. The anchors must have enough tensile capacity to resist the induced uplift force. This can occur with compression and bending, or with tension and bending.
Design checks needed for Large Moment Case (compressão + Bending or Tension + Dobra):
- Rolamento de concreto
- Base plate yielding at the bearing interface
- Base plate yielding at the tensile interface
- Anchor checks for tension
Set 3: Combined Axial Tension and Bending (Momento Baixo)
Base plates may also carry tension and moment. Although this is less common, it is still a possible scenario. It applies when the eccentricity from the tension and moment loads is small enough that the plate does not behave as a large moment case. Aqui, all of the anchors are in tension. Several methods are available for distributing the force among the anchors and are worth reviewing as further reading.
Design checks needed for Low Moment Case (Tensão + Dobra):
- Base plate yielding at the tensile interface
- Anchor checks for tension
For more information on anchors checks with tension, check this documentation on anchor design per ACI 318-19.
Calculate Base Plate Design Loads with SkyCiv
Software de design de placa de base SkyCiv performs the calculations described above, including concrete bearing, base plate yielding, anchor tension, and other connection checks. Selecione o código do projeto, enter the column and loading conditions, and generate the design results directly in your browser.
