柱之設計 Design of Columns 5

柱之設計 Design of Columns - Column load transfer from beams and slabs - Type of Columns - Strength of Short Axially Loaded Columns Column Failure by Axial Load

柱之荷重 ( 由梁及版傳遞 )Column load transfer from beams and slabs 1) Tributary area method: Half distance to adjacent columns y x Load on column = area ด  floor load Floor load = DL + LL DL = slab thickness ด  conc. unit wt. Example: x = 5.0 m, y = 4.0 m, LL = 300 kg/m 2, slab thickness = 10 cm Floor load = 0.1(2,400) = 540 kg/m 2 Load on column = (5.0)(4.0)(540) = 10,800 kg = 10.8 t

2) Beams reaction method: B1 B2 R B1 R B2 Collect loads from adjacent beam ends C1 B1B2 B3 B4

Load summation on column section for design Design section ROOF 2nd FLOOR 1st FLOOR Footing Ground level Load on pier column = load on 1st floor column + 1st floor + Column wt. Load on 1st floor column = load on 2nd floor column + 2nd floor + Column wt. Load on 2nd floor column = Roof floor + Column wt.

Buckling Defined

Euler’s Formula

Effective Length Concept

柱之種類 Type of Columns 橫箍筋 Tie Longitudinal steel 橫箍柱 Tied column 螺旋箍筋 Spiral s = pitch 螺旋箍筋柱 Spirally reinforced column

承受軸向荷重短柱之強度 Strength of Short Axially Loaded Columns Short columns are typical in most building columns.

[  F y = 0 ] From experiment: where A g = Gross area of column section A st = Longitudinal steel area Column_08

PuPu 0 Axial deformation  Initial failure Axial load Tied column Light spiral ACI spiral Heavy spiral 柱之破壞 Column Failure by Axial Load  PuPu

需要強度及強度折減係數 需要強度 U = 1.4D + 1.7L U = 0.75(1.4D + 1.7L + 1.7W) U = 0.9D + 1.3W 強度折減係數 (  ) : 螺旋箍筋柱  = 0.75 橫箍筋柱  = 0.70

柱鋼筋之配置 橫箍筋間距 (s) s ฃ  16 主筋直徑 s ฃ  48 箍筋直徑 s ฃ  柱之最小尺寸

箍筋之配置 xx x ฃ  15 cm xx x  15 cm xx x ฃ  15 cm x x xx x  15 cm x x

螺旋箍筋柱 PuPu Initial shape Final shape f2f2 Spiral f2f2 Increase of compressive strength due to lateral pressure: Good design: Strength lost by spalling = Strength gain from f 2 1

Core Spiral s h core A b f y s [  F x = 0 ] h core s f 2 = 2 A b f y f2f2

Define: ss 3 Rounding 0.42 to 0.45, ACI Code: 1) f y ฃ  4,000 kg/cm 2 2) Spiral diameter  ณ  10 mm 3) 2.5 cm ฃ  Clear spacing ฃ  7.5 cm 螺筋比 最小螺筋比