Reinforced Concrete Design

Transcription

1 3 Reinforced Concrete Design Strength of Rectangular Section in Bending Floor Framing System Load Transferred to Beam from Slab Continuous Beams and One-way Slabs Bending Moment Envelopes ACI Moment and Shear Coefficients Mongkol JIRAVACHARADET S U R A N A R E E UNIVERSITY OF TECHNOLOGY INSTITUTE OF ENGINEERING SCHOOL OF CIVIL ENGINEERING

2 Floor Framing System To transfer vertical loads on the floor to the beams and columns in a most efficient and economical way Columns Joist Spandrel Layout of Beams and Columns - Occupancy requirements - Commonly used beam size Stair - Ceiling and services requirements Stringer Floor beam or Girder

3 Loading on Beams Tributary area = Area for which the beam is supporting One-way Floor System (m =S/L < 0.5) C1 B2 ws kg/m B3 Tributary area B1 S L Floor load w kg/m 2 B1 Loading Load from B1 B3 Loading B1 = Secondary Beam B3 = Primary Beam If span of B3 is too large, more secondary beam may be used.

4 Precast Concrete Slab C1 B2 B3 S Floor load = w kg/sq.m Tributary area = 0.5SL sq.m Load on beam = 0.5wSL kg/m L

5 Two-way Slab Span ratio m = S/L D 45 o 45 o C Short span (BC): Floor load = w kg/sq.m S 45 o 45 o Tributary area = S 2 /4 sq.m Load on beam = ws/4 ws/3 kg/m A L B B C B C Long span (AB): Floor load = w kg/sq.m Tributary area = SL/2 - S 2 2 /4 = S 2 m sq.m 4 m 2 Load on beam ws 3 m kg/m 3 2

6 50 ก ก ก ก ก ก ก ก ก 10 ก ก 8 ก ก

7 CONTINUOUS BEAMS AND SLABS w w w w L L L L SHEAR: MOMENT: Methods of Analysis: - Exact analysis: slope-deflection, moment distribution - Approximate analysis: ACI shears and moments coefficients - Computer: MicroFEAP, Grasp, SUTStructor, STAAD.Pro, SAP2000

8 LOAD PATTERNS (Live Load) Use influence lines for determining load patterns that will give the maximum shear force and bending moment A Influence line for moment at A Load pattern for max. positive moment at A B Influence line for moment at B Load pattern for max. negative moment at B

9 LOAD PATTERN IN FRAME Frame Example: Maximum +M at point B Draw qualitative influence lines Resulting pattern load: checkerboard pattern

10 Arrangement of Live Loads ACI Sec : It shall be permitted to assume that the arrangement of live load d is limited to combinations of: Factored dead load on all spans with full factored live load on o two adjacent spans. Factored dead load on all spans with full factored live load on alternate spans.

11 Moment Envelopes The moment envelope curve defines the extreme boundary values of bending moment along the beam due to critical placements of design live loading.

12 Moment Envelopes LL DL

13 Moment Envelopes Example Given following beam with a dead load of 1 t/m and live load 2 t/m obtain the shear and bending moment envelopes A 6 m B 6 m C

14 Moment Envelopes Example CASE 1 : DL(full) + LL(full) LL DL A 6 m B 6 m C kips Shear Diagram ft k-ft Moment Diagram ft

15 Moment Envelopes Example CASE 2 : DL(full) + LL(half) LL DL A 6 m B 6 m C kips Shear Diagram ft k-ft Moment Diagram ft

16 Moment Envelopes Example The shear envelope Shear Envelope kips Minimum Shear Maximum Shear ft

17 Moment Envelopes Example The moment envelope Moment Envelope k-ft ft Minimum Moment Maximum Moment

18 ACI Approximated Coefficients for Moments and Shears ก ก : 1) 2 2) ก ก ก ก 20% 3) ก ก 4) ก ก 3 ก ก 5) ก

19 13.1 ACI (ก) ก 1) - ก w u l n2 /11 - ก ก w u l n2 /14 2) w u l n2 /16 ( ) 1) ก ก - 2 w u l n2 /9 - กก 2 w u l n2 /10 2) w u l n2 /11

20 ( ) ( ) 3) ก - ก w u l n2 /12 - > 8 w u l n2 /12 4) ก - w u l n2 /24 - w u l n2 /16 ( ) 1) ก ก 1.15 w u l n /2 2) w u l n /2

21 (a) กก (Spandrel) : 0 1/11 : 1/16 1/14 1/10 1/11 1/16 1/11 1/11 : 1/24 1/14

22 ก ก

23 (b) : 0 1/11 : 1/16 1/14 1/9 1/9 1/14 1/16 : 1/24 1/14 (c) ก 3 1/12 1/14 1/12 1/12 1/16 1/12 1/12

24 (d) กก 8 1/12 1/14 1/12 1/12 1/16 1/12 1/12

25 Ex3.1: A two span beam is supported by spandrel beams at the outer edges and by a column in the center. Dead load (including beam weight) is 1.5 t/m and live load is 3 t/m on both beams. Calculate all critical service-load shear forces and bending moments for the beams. The torsional resistance of the spandrel beam is not sufficient to cause restraint of beam ABC at the masonry walls. Masonry Wall D C L E C L Masonry Wall B B 6 m 6.5 m A B C Check conditions (a) Loads are uniformly distributed, (b) LL/DL = 3/1.5 = 2 < 3, (c) (L 2 L 1 )/L 1 = (6.5 6)/6 = < 0.2 Bending Moments M AB = -4.5(6) 2 /24 = t-m, M BA = -4.5(6.25) 2 /9 = t-m, M CB = -4.5(6.5) 2 /24 = t-m, M BC = -4.5(6.25) 2 /9 = t-m, M D = 4.5(6) 2 /11 = 14.7 t-m, M E = 4.5(6.5) 2 /11 = 17.3 t-m

26 Masonry Wall D C L E C L Masonry Wall B B 6 m 6.5 m A B C Shear Forces V A = 4.5(6)/2 = 13.5 tons, V C = 4.5(6.5)/2 = 14.6 tons, V B = 1.15(4.5)(6)/2 = 15.5 tons, V B = 1.15(4.5)(6.5)/2 = 16.8 t-m Reactions R A = V A = 13.5 tons, R B = V B + V B = = 32.3 tons, R C = V C = 14.6 tons

27 Gravity & Lateral loads on Portal Frame W L R Portal frame subjected to gravity loads: L R Portal frame subjected to lateral loads: L R L R

28 Rigid frame deflections forces and deformations caused by external shear

29 Bending Moment in Column & Beam