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Design Code – American

Reference:

Load : American Society of Civil Engineers, ASCE 7-16
Concrete: American Concrete Institute, ACI 318-19
Steel: American Institute of Steel Construction, AISC 360-16


Load Combinations:

The Basic load combinations under ASCE 7-16 applies are :

  1. \(1.4D\)
  2. \(1.2D + 1.6L + 0.5(L_{r} \text{ or } S \text{ or } R)\)
  3. \(1.2D + 1.6(Lr \text{ or } S \text{ or } R) + (L \text{ or } 0.5W)\)
  4. \(1.2D + 1.0W + L + 0.5(Lr \text{ or } S \text{ or } R)\)
  5. \(1.2D + 1.0E + L + 0.2S\)
  6. \(0.9D + 1.0W\)
  7. \(0.9D + 1.0E\)

where :

\(D\) = dead load
\(L\) = live load
\(L_{r}\) = roof live load
\(S\) = Snow load
\(R\) = Rain load
\(E\) = Earthquake
\(W\) = Wind load


Concrete bearing check:

Concrete design bearing strength in compression is designed according to AISC 360-16 Eq. J8-2.

\( F_{b} = \phi _{bearing} \times 0.85 \times f’_{c} \times \sqrt{ \frac{ A_{2} }{ A_{1} } } \leq F_{b, limit} = 1.70 \times f_{c} \times A_{1} \)

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 )


Weld check:

The weld group strength check are in accordance of AISC 360-16 J2

\( (i) R_{n} = R_{nwl} + R_{nwt} \)

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.


Anchor check:

The Anchor checks applies using code provisions of ACI 318-19 under Chapter 17.

Anchor rods are designed according to AISC 360-16 – J9 and ACI 318-19 – Chapter 17. 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 side-face blowout strength, \( \phi N_{sb} \).
  • 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 ACI 318-19 – 17.6.1.2 and 17.7.1 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 ACI 318-19 – 17.6.2 and 17.7.1 as

\( \phi N_{cbg} = \phi \frac{ A_{Nc} }{ A_{Nco} } \psi_{ec,N} \psi_{ed,N} \psi_{c,N} \psi_{cp,N} N_{b} \rightarrow \) equation 17.6.2.ab

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.

\( \psi_{ec,N} \) – Breakout eccentricity factor in tension.

\( \psi _{ec,N} = \frac{1.00}{ 1 + \frac{e^{‘}_{N}}{1.5 h_{ef}} } \leq 1.00 \rightarrow \) equation 17.6.2.3.1

\( \psi_{ed,N} \) – Breakout effect factor in tension.

(a) \( \text{if } C_{a,min} \geq 1.5h_{ef} \text{ then } \psi _{ed,N} = 1.00 \) equation 17.6.2.4.1a

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 17.6.2.4.1b

\( \psi_{c,N} \) – 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 ACI 318-19 – 17.6.3 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:

\( N_{p} = 8A_{brg}f^{‘}_{c}\) equation 17.6.3.2.2a

For non-cracked concrete:

\( N_{p} = 0.9f^{‘}_{c}e_{h}d_{a} \rightarrow \) equation 17.6.2.2.b

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.

Concrete side-face blowout strength

Factored concrete side-face blowout strength of an anchor is defined in ACI 318-19 – 17.6.4 as

\( \phi N_{sb} = 160C_{a1}\sqrt{A_{brg}}\lambda _{a} \sqrt{f^{‘}_{c} } \rightarrow \) equation 17.6.4.1

where:

\( f^{‘}_{c} \) – specified compressive strength of concrete.
\( A_{brg} \) – net bearing area of the head of stud, anchor bolt or headed deformed bar.
\( \lambda_{a} \) – modification factor to reflect the reduced mechanical properties of lightweight concrete in certain concrete anchorage application.

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