Sensitivity Data Driven Composite Floor Structural Optimization for Tall Office Buildings

Abstract

In tall office buildings, steel beam composite floor system is a popular solution for floor systems as it is known for requiring less construction time and having good weight-to-strength ratio. However, despite being a relatively light-weight floor system, steel beams in composite floor systems are still accountable for a large percentage of buildings’ self-weight. Therefore, optimization of this floor system design is still required, especially for tall buildings, and it can be achieved by reducing the weight of steel beam supporting the composite deck. In this paper, optimization methods, Multiple Decomposition Method and Sensitivity Data Driven Algorithm, are employed to design and optimize a large span steel beams supporting deck floor of a tall office building. Based on Multiple Decomposition Method, the composite floor’s beams are divided into three substructure levels. To global structural performance, the 1st level which consists of the entire composite deck floor aims to achieve floor the serviceability performance. Subsequently, the 2nd level involves serviceability requirement of composite beams within the floor. Lastly, the 3rd level consists of structural elements such as the composite deck, steel beams, and shear studs, and the optimization problem is related to sizing the cross-section dimensions of each beam to meet the design requirements from both the 2nd level and 3rd level. In addition, Sensitivity Data Driven Algorithm is also used to further determine design constraint sensitivity coefficients to design variables as guidance to examine optimum beam sizing proportion.

Appendix A

This appendix provides necessary detailed formulations for composite steel beam analysis.

Limiting width-thickness ratios for flanges of doubly I-shaped built-up sections

$$ {\text{Compact web}}:({\text{H}} - {\text{2T}}_{{\text{f}}} )/{\text{T}}_{{\text{w}}} \le \lambda_{p} = 3.76\sqrt {\frac{{E_{s} }}{{F_{y} }}} $$

(AISC Table B4.1b)

$$ {\text{Compact flange}}:(0.5{\text{B)}}/{\text{T}}_{{\text{f}}} \le \lambda_{p} = 0.38\sqrt {\frac{{E_{s} }}{{F_{y} }}} $$

(AISC Table B4.1b)

Notice: In this study case, T_f chosen for design is 10% larger than T_f required by AISC specifications.

Steel beam section properties

$$ {\text{A}}_{{\text{s}}} = {\text{BT}}_{{\text{f}}} + ({\text{H}} - 2{\text{T}}_{{\text{f}}} ){\text{T}}_{{\text{w}}} $$

$$ {\text{I}}_{{{\text{s}}.{\text{x}}}} = (1/12)({\text{BH}}^{3} ) - (1/12)({\text{B}} - {\text{T}}_{{\text{w}}} ).({\text{H}} - 2\,{\text{T}}_{{\text{f}}} )^{3} $$

$$ {\text{Z}}_{{\text{x}}} = (1/4){\text{BH}}^{2} $$

Transformed concrete section properties

${\text{B}}_{{{\text{eff}}}} = \min$ (min beam spacing. 2 the smallest distance to the nearest slab edge, L/4) (AISC Sec I3.1a)

$$ {\text{B}}_{{{\text{eff.Tr}}}} = \upalpha {\text{B}}_{{{\text{eff}}}} $$

$$ \upalpha = {\text{E}}_{{\text{c}}} /{\text{E}}_{{\text{s}}} $$

$$ {\text{A}}_{{{\text{c.tr}}}} = {\text{B}}_{{{\text{eff.tr}}}} \,{\text{H}}_{{{\text{con}}}} $$

$$ I_{{{\text{c.tr.x}}}} = \, (1/12){\text{B}}_{{{\text{eff.tr}}}} \,{\text{H}}_{{{\text{con}}}}^{3} $$

Full composite beam section properties

$$ \overline{{\text{Y}}} = {\text{(A}}_{{{\text{c.tr}}}} ({\text{H}}_{{{\text{con}}}} /2) + {\text{A}}_{{\text{s}}} .({\text{H}}_{{{\text{deck.total}}}} + {\text{H}}/2))/({\text{B}}_{{{\text{eff.tr}}}} {\text{H}}_{{{\text{con}}}} + {\text{A}}_{{\text{s}}} ) $$

$$ {\text{I}}_{{{\text{full.com.x}}}} = {\text{I}}_{{{\text{sx}}}} + {\text{A}}_{{\text{s}}} (({\text{H}}_{{{\text{deck.total}}}} + 0.5\,{\text{H}}) - \overline{{\text{Y}}} )^{2} + {\text{I}}_{{{\text{c.tr.x}}}} + {\text{A}}_{{{\text{c.tr}}}} .((0.5\,{\text{H}}_{con} ) - \overline{{\text{Y}}} {)}^{{2}} $$

Total deflection after composite action

${\text{I}}_{{{\text{eff.x}}}} = {\text{I}}_{{{\text{full.com.x}}}}$ (100% composite action and shoring during construction)

$$ \Delta_{{{\text{max.mid}}}} = \frac{5}{48}\frac{{({\text{M}}_{{{\text{dead}}}} + {\text{M}}_{{\text{super-dead}}} + {\text{M}}_{{{\text{liveload}}}} ){\text{L}}^{2} }}{{{\text{E}}\,{\text{I}}_{{{\text{eff.x}}}} }} $$

$$ \Delta_{{{\text{allowable}}}} = \frac{{\text{L}}}{240} $$

Design composite plastic moment capacity for positive bending

Assuming shear studs provide 100% composite action.

$$ {\text{C}} = \min ({\text{A}}_{{\text{s}}} {\text{F}}_{{\text{y}}} ,0.85\,{\text{f}}_{{\text{c}}}^{\prime } \,{\text{H}}_{{{\text{con}}}} \,{\text{B}}_{{{\text{eff}}}} ) $$

(AISC C-I3-6, C-I3-7)

$$ {\text{a}} = \frac{{\text{C}}}{{0.85\,{\text{f}}_{{\text{c}}}^{\prime } \,{\text{B}}_{{{\text{eff}}}} }} $$

(AISC C-I3-6, C-I3-9)

$$ {\text{M}}_{{\text{n}}} = {\text{C}}\left( {\frac{{\text{H}}}{2} + {\text{H}}_{{{\text{deck.total}}}} - \frac{{\text{a}}}{2}} \right) $$

(AISC C-I3-10)

$$\upphi {\text{M}}_{{\text{n}}} =\upphi _{{{\text{bcpp}}}} {\text{M}}_{{\text{n}}} = 0.9\,{\text{M}}_{{\text{n}}} $$

(AISC Sec. I3.2)

Design shear strength in the major direction

For I-shaped section,

$$\upphi _{{\text{v}}} {\text{V}}_{{\text{n}}} =\upphi _{{\text{v}}} 0.6{\text{A}}_{{\text{w}}} {\text{F}}_{{\text{y}}} {\text{C}}_{{{\text{v}}1}} $$

(AISC G2-1)

$$ \begin{aligned}{\upphi }_{{\text{v}}} & = 1.0\quad {\text{if}}({\text{H}} - 2{\text{T}}_{{\text{f}}} )/{\text{t}}_{{\text{w}}} \le 2.24\sqrt {\frac{{{\text{E}}_{{\text{s}}} }}{{{\text{F}}_{{\text{y}}} }}} \\ & \quad 0.9\quad {\text{if}}({\text{H}} - 2{\text{T}}_{{\text{f}}} )/{\text{t}}_{{\text{w}}} > 2.24\sqrt {\frac{{{\text{E}}_{{\text{s}}} }}{{{\text{F}}_{{\text{y}}} }}} \\ \end{aligned} $$

(AISC G2-1a)

$$ \begin{aligned} {\text{C}}_{{{\text{v}}1}} & = 1.0\quad {\text{if}}({\text{H}} - 2{\text{T}}_{{\text{f}}} )/{\text{t}}_{{\text{w}}} \le 1.10\sqrt {\frac{{5.34\,{\text{E}}_{{\text{s}}} }}{{{\text{F}}_{{\text{y}}} }}} \\ & \quad \frac{{1.1\sqrt {5.34\,{\text{E}}_{{\text{s}}} /{\text{F}}_{{\text{y}}} } }}{{({\text{H}} - 2{\text{T}}_{{\text{f}}} )/{\text{t}}_{{\text{w}}} }}\quad {\text{if}}({\text{H}} - 2{\text{T}}_{{\text{f}}} )/{\text{t}}_{{\text{w}}} > 2.24\sqrt {\frac{{5.34\,{\text{E}}_{{\text{s}}} }}{{{\text{F}}_{{\text{y}}} }}} \\ \end{aligned} $$

(AISC G2-3, G2-4)

$$ {\text{A}}_{{\text{w}}} = {\text{HT}}_{{\text{w}}} $$

(AISC G2-1)