Below is an example of some Philippine Code Base Plate Calculations that are commonly used in base plate design. Often when designing base plates, we will consider a few different checks relating to the various components of a base plate, namely:
- The Concrete base – generally checked against bearing and compression forces in reference to NSCP 2015
- The Welds – welds need to be checked, to ensure they provide adequate restraint and do not fail under stress to NSCP 2015
- Anchor Bolts – can fail due to a number of reasons, as shown below in the example anchor bolt design calculations to NSCP 2015
- Steel Member (Column) checks – usually based on local steel design standards
Currently, the Steel Base Plate Design module implements the following checks below. The paid version of this software, includes detailed step-by-step calculations, so that engineers can review exactly how these calculations are made!
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Load Combinations:
The Steel Base Plate Design the uses factored load combinations under NSCP 2015 applies as follows:
- \(1.4D\)
- \(1.2D + 1.6L + 0.5(L_{r} \text{ or } R)\)
- \(1.2D + 1.6(Lr \text{ or } R) + (f1L \text{ or } 0.5W)\)
- \(1.2D + 1.0W + f1L + 0.5(Lr \ \text{ or } R)\)
- \(1.2D + 1.0E + f1L\)
- \(0.9D + 1.0W\)
- \(0.9D + 1.0E\)
where :
\(D\) = dead load
\(L\) = live load
\(L_{r}\) = roof live load
\(R\) = Rain load
\(E\) = Earthquake
\(W\) = Wind load
\(f_{1}\) = Live load factor (Default value = 1, See NSCP 2015 Section 203.3.1)
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NSCP 2015 Concrete bearing check:
The Steel Base Plate Design checks the Concrete bearing strength (compression) design in according to NSCP 2015 Eq. 510.8-2.
\( F_{b} = \phi _{bearing} \times 0.85 \times f’_{c} \times \sqrt{ \frac{ A_{2} }{ A_{1} } } \leq F_{b, limit} = 1.70 \times f_{c} \times A_{1} \)
where:
\( f’_{c} \) – concrete compressive strength
\( A_{1} \) – base plate area in contact with concrete surface
\( A_{2} \) – concrete supporting surface
\( \phi_{bearing} \) – resistance factor for concrete ( default value= 0.65 )
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NSCP 2015 Weld Design Check:
The Steel Base Plate Design checks weld design accordance to NSCP 2015 Equation 510.2-3
\( (i) R_{n} = R_{nwl} + R_{nwt} \)
or
\( (ii) R_{n} = 0.85R_{nwl} + 1.5R_{nwt} \)
where:
\(R_{nwl} \) = total nominal strength of longitudinal loaded fillet welds.
\(R_{nwt} \) = total nominal strength of transversely loaded fillet welds.
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NSCP 2015 Anchor Design Check:
The Steel Base Plate Design checks Anchor parameters applies using code provisions of NSCP 2015 Section 417 | Anchoring to Concrete.
The following resistances of anchor bolts are evaluated:
- Steel strength of anchor in tension and shear, \( \phi N_{sa} \) and \( \phi V_{sa} \).
- Concrete breakout strength in tension and shear, \( \phi N_{cbg} \) and \( \phi V_{cbg} \).
- Concrete pullout strength, \( \phi N_{p} \).
- Concrete pryout strength of anchor in shear, \( \phi V_{cp} \).
Steel strength of anchor in tension and shear
Factored steel strength of anchor in tension and shear is determined according to NSCP 2015 Section 417.4.1 as
For Tension
\( \phi _{tension, anc} N_{sa} = \phi _{tension, anc} A_{se,N}f_{uta} \rightarrow \) equation 17.6.1.2
For Shear
\( \phi _{shear, anc} V_{sa} = \phi _{shear, anc} 0.6A_{se,V}f_{uta} \rightarrow \) equation 17.7.1.2b
where:
- \( \phi _{tension, anc} \) – strength reduction factor for anchors in tension ( default value = 0.75 )
- \( \phi _{shear, anc}\) – strength reduction factor for anchors in shear ( default value = 0.65 )
- \( A_{se,N}\) – is the effective cross-sectional area of an anchor in tension.
- \( A_{se,V}\) – is the effective cross-sectional area of an anchor in shear.
- \( f_{uta}\) – specified tensile strength of anchor steel and shall not be greater than \(1.9f_{ya}\) and 125 ksi (861.845 Mpa)
Concrete breakout strength
Factored concrete breakout strength of anchor in tension and shear is determined according to NSCP 2015 Equation 417.4.2.1b and NSCP 2015 Equation 417.5.2.1b as
\( \phi N_{cbg} = \phi \frac{ A_{Nc} }{ A_{Nco} } \psi_{ec,N} \psi_{ed,N} \psi_{c,N} \psi_{cp,N} N_{b} \rightarrow \) 417.4.2.1b
where:
\( \phi \) – strength reduction factor for anchors in tension ( default value = 0.75 ).
\( A_{Nc} \) – projected concrete failure of a single or group anchors.
\( A_{Nco} \)- project concrete failure area of a single anchor, for calculation of strength in tension if not limited by edge distance or spacing.
\( \psi_{ec,N} \) – Factor Used to Modify Tensile Strength of Anchors Based on Eccentricity of Applied Loads.
\( \psi _{ec,N} = \frac{1.00}{ 1 + \frac{2 \times e^{‘}_{N}}{3 \times h_{ef}} } \leq 1.00 \rightarrow \) Equation 417.4.5.3
\( \psi_{ed,N} \) – Factor Used to Modify Tensile Strength of Anchor.
(a) \( \text{if } C_{a,min} \geq 1.5h_{ef} \text{ then } \psi _{ed,N} = 1.00 \)
and
(b) \( \text{if } C_{a,min} < 1.5h_{ef} \text{ then } \psi _{ed,N} = 0.70 + 0.3\frac{C_{a,min}}{1.5h_{ef}} \) Equation 417.4.2.5b
\( \psi_{c,N} \) – Breakout cracking factor in tension.
\( \psi _{c,N} = 1.25 \) for cast-in anchors
\( \psi_{cp,N} \) – Breakout splitting factor in tension.
(a) \( \text{if } C_{a,min} \geq C_{ac} \text{ then } \psi _{cp,N} = 1.00 \) equation 17.6.2.4.1a
and
(b) \( \text{if } C_{a,min} < C_{ac} \text{ then } \psi _{cp,N} = \frac{ C_{a,min} }{ C_{ac}} \geq \frac{ 1.5h_{ef} }{ C_{ac} } \) equation 17.6.2.4.1b
\( N_{b} \) – basic concrete breakout strength in tension of a single anchor in cracked concrete.
Concrete pullout strength
Factored concrete pullout strength of an anchor is defined in NSCP 2015 Equation 417.4.3.4 as
ϕNpn = ϕΨc,P Np
where:
\( \phi \) – strength reduction factor for anchors in tension ( default value = 0.70 ).
\( \psi _{c, P} \) – modification factor for concrete condition
For cracked concrete:
\( \psi _{c, P} \) = 1.0
For non-cracked concrete:
\( \psi _{c, P} \) = 1.4
\( N_{p} \) – Anchor pullout strength
For cracked concrete:
\( N_{p} = 8A_{brg}f^{‘}_{c}\rightarrow \) Equation 417.4.3.4
For non-cracked concrete:
\( N_{p} = 0.9f^{‘}_{c}e_{h}d_{a} \rightarrow \) Equation 417.4.3.5
where \( 3d_{a} \leq e_{h} \leq 4.5d_{a} \)
\( f^{‘}_{c} \) – specified compressive strength of concrete.
\( A_{brg} \) – net bearing area of the head of stud, anchor bolt or headed deformed bar.
\( e_{h} \) – distance from the inner surface of the shaft of a J-bolt or L-bolt to the outer tip of the J- or L-bolt.
\( d_{a} \) – outside diameter of anchor or shaft diameter of headed stud, headed bolt, or hooked bolt.
