Method 2 of two-way slabs

Appendix c of SBC304

1 vs 2 M-negative M-Positive 1-load transfer 2-load transfer

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One-way versus Two-way

2bbb wlCM

lb

la

2aaa wlCM

lb

la

2aaa wlCM

Two-way coefficients depend on aspect ratio m=la/lb, and continuity. Accordingly there are 9 cases and m is in the range of 1 to 0.5. Also coefficients of dead load are different from those of live load for positive

moments. Hence, there are three tables of coefficients: Table 2 to 4.

One-waytwo-way

For one-way, load is carried in the short

direction only.

For two-way, load is carried in two directions.

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Negative moment

2,, aneganega wlCM 2

,, bnegbnegb wlCM

lb

lb

la

lb

la

Ma-neg

Mb-

neg

Wd= 1.4 *6.08=8.512; Wl=1.7*3=5.1la=5.6 m; Lb=7.6 mInterior panel, case2m=la/lb=0.737

Ca_neg= 0.070Ma,neg= 0.07*5.62*13.612=30 kN-m

Section design

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Positive moment

2,,, bdlbdlposb wlCM

2,,, adladlposa wlCM

2,,, allallposa wlCM

2,,, bllbllposb wlCM

lb

la

lb

laMa-pos

Mb-

pos

Wd= 1.4 *6.08=8.512; Wl=1.7*3=5.1la=5.6 m; Lb=7.6 mInterior panel, case2m=la/lb=0.737

Ca_pos_dl= 0.029Ma,pos_dl= 0.029*5.62*8.512=7.615 kN-mCa_pos_ll= 0.046Ma,pos_ll= 0.046*5.62*5.1=7.365 kN-mMa_pos=7.615+7.365=14.98 kN-m

Ca_dl Ca_llCb_dl Cb_ll

Section design

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Table 2: Coefficients for negative moments in slabs1 2 3 4 5 6 7 8 9

Interior panel, case 2 la=5.6, lb=7.6, m=0.737

0.700.074

Example

By interpolation:Ca_neg=0.074+(0.069-0.074)/(0.75-0.7)*(0.737-0.7)=0.070

Ca,neg: 0.750.069

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Table 3: Coefficients for dead-load positive moments in slabs 1 2 3 4 5 6 7 8 9

Interior panel, case 2 la=5.6, lb=7.6, m=0.737

0.700.030

Example

By interpolation:Ca_dl=0.030+(0.028-0.030)/(0.75-0.7)*(0.737-0.7)=0.029

Ca,dl: 0.750.028

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Table 4 Coefficients for live-load positive moments in slabs

1 2 3 4 5 6 7 8 9

Interior panel, case 2 la=5.6, lb=7.6, m=0.737

0.700.049

Example

By interpolation:Ca_ll=0.049+(0.045-0.049)/(0.75-0.7)*(0.737-0.7)=0.046

Ca,ll: 0.750.045

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Case 2-4-8-9

LAB

X

Y

C

1 3 42

A

L34L23L12

LCD

B

D

Geometry:

L12=L34=8.2 m; L23= 8.0 m ;LAB=LCD=6.15 m; Lbc=6.0 m

Beam width= 0.4 m; Girder width= 0.4 m

LBC

Case 4

Case 8Case 4

Case 9

Case 4

Case 4

4

9

2

8

Case 9

Case 8

Case 2

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Two-way slab layoutcases: 1-3-4-5-6-7

LAB

X

Y

C

1 3 42

A

L34L23L12

LCD

B

D

Geometry:

L12=L34=8.2 m; L23= 8.0 m ;LAB=LCD=6.15 m; Lbc=6.0 m

Beam width= 0.3 m; Girder width= 0.4 m

LBC

1

Case 1

Case 3Case 4

Case 5

Case 6

Case 7

34

5

6

7

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Animation of two-way slab load

dividelong

shortPanel

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Slab-beam Load transfer

Ws Ws

MW

Masonry wall =bm*hm*m

SL

Dwd

direct dead load on beam =h*b*c+b*super imposed dead load

tw tw

b b

h

ws*tw

tw

tw

1

1

1-1

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Section designGiven / assumed data f_y 420.00 MPab_w= 1000.00 mm f_c 25.00 MPah= 170.00 mm Live= 3.00 kN/m2

Super_d 2.00 kN/m2

load on 1-m slabservice FactoredLive= 3.00 kN/m Dead= 8.512 kN/mSuper_d 2.00 kN/m Live= 5.1 kN/mweight= 4.08 kN/m Total= 13.612 kN/m

negative positived_b 14 10d 143 145

Mu 30.0 15.0

Rn 1.63 0.79r 0.0040 0.0019A_s 578.4 278.6As_min 306.0 306.0spacing 266.1 256.7max spacing 300 300selected spacing250 250

la 5.6 m ca_neg ca_pos_dlca_pos_ lllb 7.6 0.75 0.069 0.028 0.045m 0.737 0.7 0.074 0.03 0.049

0.737 0.070 0.029 0.046

Ma 30.016 7.615 7.365Ma_neg 30.016Ma_pos 14.980