Designing Procedure of Slab through Moment Coefficient Method

This article briefly explains the structural design of slabs using the moment coefficient method. Before starting the design, the structure designer completes the following tasks:

Create a beam framing plan: Mark the location of the proposed beams on the plan and obtain approval from the Architect for the beam placement.
Determine the slab type: Verify whether the slab is one-way or two-way by calculating the ratio of the longer span (Ly) to the shorter span (Lx).
- If Ly/Lx > 2, the slab is one-way.
- If Ly/Lx < 2, the slab is two-way.

Here:

Ly = longer span
Lx = shorter span

Contents

Design Procedure of One-way Slab (Ly/L_x> 2)

when Ly/L_x> 2, the slab is designed as a one-way slab. In one-way slabs, loads are distributed in the longer direction.

Minimum thickness of slab

First, determine the minimum thickness of the one-way slab. Next, ensure the slab thickness is equal to or greater than the minimum required to control deflection. Otherwise, deflection must be checked against the allowable limits. Additionally, the minimum criteria for one-way slab thickness are outlined in the table below (Refer to Table 1):

Support condition	h_min
Simply supported	L_x/20
One end continuous	L_x/24
Two end continuous	L_x/28
Cantilever	L_x/10

Table: 1 Minimum thickness of one-way slab

Loads on slab

Dead load

Self wt (KN/m²) = (unit wt of material) × thickness of slab.

Finishes (KN/m²) = (unit wt of material) × finishes thickness

Live Load

Pick up live load according to floor/ roof occupancy

Moment Calculation

Pick up the moment coefficient according to the support condition from the below table (Refer Table 2).

Support condition	Positive moment Coefficient		Negative moment Coefficient
	Exterior span	Interior span	Exterior support	Interior support
Simply supported slab	1/8	1/8	–	–
Two Span slab	1/14	1/14	1/16	1/9
More then two span slab	1/14	1/16	1/16	1^st interior support	2^nd interior support
				1/10	1/11

Table 2: Moment coefficient for one-way slab

here;

Calculation for area of steel

Calculate R_u(in Mpa) using the formula for each Mu(i.e. support and span moment)

Calculate steel ratio (ρ) using the below formula for each R_u

here;

Calculate the Area of steel (in mm2/m) using the below formula for each ρ

Calculate the minimum area (in mm²/m) of steel

Compare each As with As_minand select the greater values

Calculate the spacing of bars (in mm) using the governing value of each As

Design Procedure of Two-way Slab (Ly /Lx < 2)

If Ly/L_x< 2, Slab is designed as a two-wayslab. In two ways slab loads are distributed in both directions.

Minimum thickness of slab

Calculate the minimum thickness of the slab using the formula provided below. Ensure the slab thickness is equal to or greater than the calculated minimum to effectively control deflection. If the thickness is less, deflection must be verified against the allowable limits.

Loads on slab

Dead load

Self wt (KN/m²) = (unit wt of material) × thickness of slab.

Finishes (KN/m²) = (unit wt of material) × finishes thickness.

Live Load

Pick up live load according to floor/ roof occupancy

Moment Calculation

Calculate positive and negative moments (In KN-m/m) by taking the moment coefficient from the provided table below. These coefficients are based on the continuity or discontinuity of the slab in all directions.

Positive (+ve) moment

For positive moments (i.e. span moments in both directions) dead and live load coefficients are different, which are provided in the below table (Refer Table:3):

Ratio m = Lx/Ly		All Edges Conti-nious	One Short Edge Disco-ntinious	One Long Edge Disco-ntinio-us	Two Adjacent Edges Discon-tinious	Two Short Edges Discont-inious	Two Long Edges Discon-tinious	One Long Edge Conti-nious	One Short Edge Contin-ious	Four Edges Disco-ntinio-us
1	C_X(DL)	0.018	0.023	0.020	0.027	0.027	0.018	0.033	0.027	0.036
	C_y(DL)	0.018	0.020	0.023	0.027	0.018	0.027	0.027	0.033	0.036
	C_x(LL)	0.027	0.030	0.028	0.032	0.032	0.027	0.035	0.032	0.036
	C_y(LL)	0.027	0.028	0.030	0.032	0.027	0.032	0.032	0.035	0.036
0.95	C_X(DL)	0.020	0.024	0.022	0.030	0.028	0.021	0.036	0.031	0.040
	C_y(DL)	0.016	0.017	0.021	0.024	0.015	0.025	0.024	0.031	0.033
	C_x(LL)	0.030	0.032	0.031	0.035	0.034	0.031	0.038	0.036	0.040
	C_y(LL)	0.025	0.025	0.027	0.029	0.024	0.029	0.029	0.032	0.033
0.9	C_X(DL)	0.022	0.026	0.025	0.033	0.029	0.025	0.039	0.035	0.045
	C_y(DL)	0.014	0.015	0.019	0.022	0.013	0.024	0.021	0.028	0.029
	C_x(LL)	0.034	0.036	0.035	0.039	0.037	0.035	0.042	0.040	0.045
	C_y(LL)	0.022	0.022	0.024	0.026	0.021	0.027	0.025	0.029	0.029
0.85	C_X(DL)	0.024	0.028	0.029	0.036	0.031	0.029	0.042	0.040	0.050
	C_y(DL)	0.012	0.013	0.017	0.019	0.011	0.022	0.017	0.025	0.026
	C_x(LL)	0.037	0.039	0.040	0.043	0.041	0.040	0.046	0.045	0.050
	C_y(LL)	0.019	0.020	0.022	0.023	0.019	0.024	0.022	0.026	0.026
0.8	C_X(DL)	0.026	0.029	0.032	0.039	0.032	0.034	0.045	0.045	0.056
	C_y(DL)	0.011	0.010	0.015	0.016	0.009	0.020	0.015	0.022	0.023
	C_x(LL)	0.041	0.042	0.044	0.048	0.044	0.045	0.051	0.051	0.056
	C_y(LL)	0.017	0.017	0.019	0.020	0.016	0.022	0.019	0.023	0.023
0.75	C_X(DL)	0.028	0.031	0.036	0.043	0.033	0.040	0.048	0.051	0.061
	C_y(DL)	0.009	0.007	0.013	0.013	0.007	0.018	0.012	0.020	0.019
	C_x(LL)	0.045	0.046	0.049	0.052	0.047	0.051	0.055	0.056	0.061
	C_y(LL)	0.014	0.013	0.016	0.016	0.013	0.019	0.016	0.020	0.019
0.7	C_X(DL)	0.030	0.033	0.040	0.046	0.035	0.046	0.051	0.058	0.068
	C_y(DL)	0.007	0.006	0.011	0.011	0.005	0.016	0.009	0.017	0.016
	C_x(LL)	0.049	0.050	0.054	0.057	0.051	0.057	0.060	0.063	0.068
	C_y(LL)	0.012	0.011	0.014	0.014	0.011	0.016	0.013	0.017	0.016
0.65	C_X(DL)	0.032	0.034	0.044	0.050	0.036	0.054	0.054	0.065	0.074
	C_y(DL)	0.006	0.005	0.009	0.009	0.004	0.014	0.007	0.014	0.013
	C_x(LL)	0.053	0.054	0.059	0.062	0.055	0.064	0.064	0.070	0.074
	C_y(LL)	0.010	0.009	0.011	0.011	0.009	0.014	0.010	0.014	0.013
0.6	C_X(DL)	0.034	0.036	0.048	0.053	0.037	0.062	0.056	0.073	0.081
	C_y(DL)	0.004	0.004	0.007	0.007	0.003	0.011	0.006	0.012	0.010
	C_x(LL)	0.058	0.059	0.065	0.067	0.059	0.071	0.068	0.077	0.081
	C_y(LL)	0.007	0.007	0.009	0.009	0.007	0.011	0.008	0.011	0.010
0.55	C_X(DL)	0.035	0.037	0.052	0.056	0.038	0.071	0.058	0.081	0.088
	C_y(DL)	0.003	0.003	0.005	0.005	0.002	0.009	0.004	0.009	0.008
	C_x(LL)	0.062	0.063	0.070	0.072	0.063	0.080	0.073	0.085	0.088
	C_y(LL)	0.006	0.006	0.007	0.007	0.005	0.009	0.006	0.009	0.008
0.5	C_X(DL)	0.037	0.038	0.056	0.059	0.039	0.080	0.061	0.089	0.095
	C_y(DL)	0.002	0.002	0.004	0.004	0.001	0.007	0.003	0.007	0.006
	C_x(LL)	0.066	0.067	0.076	0.077	0.067	0.088	0.078	0.092	0.095
	C_y(LL)	0.004	0.004	0.005	0.005	0.004	0.007	0.005	0.007	0.006

Table 3: Positive Moment Coefficient of Two-way slab for Dead and Live Load

Moments in both directions are calculated using the below formulas:

For the Main bar parallel to the shorter direction

M_u1(+ve) = (C_X(DL)× W_u(DL)× L_X² )+ (C_X(LL)× W_u(LL)× L_x² )

For the Main bar parallel to the longer direction

M_u2(+ve) = (C_y(DL)× W_u(DL)× L_y² )+ (C_y(LL)× W_u(LL)× L_y² )

Negative(-ve) moment

Negative moment coefficients are the same for dead and live, which are provided in the below table (Refer Table: 4)

Ratio m = Lx/Ly		All Edges Contini-ous	One Short Edge Discont-inious	One Long Edge Discont-inious	Two Adjacent Edges Discont-inious	Two Short Edges Disco-ntinio-us	Two Long Edges Disco-ntinio-us	One Long Edge Conti-nious	One Short Edge Conti-nious	Four Edges Disco-ntinio-us
1	C_x(DL+LL)	0.045	0.061	0.033	0.050	0.075		0.071
1	C_y(DL+LL)	0.045	0.033	0.061	0.050		0.076		0.071
0.95	C_x(DL+LL)	0.050	0.065	0.038	0.055	0.079		0.075
0.95	C_y(DL+LL)	0.041	0.029	0.056	0.045		0.072		0.067
0.9	C_x(DL+LL)	0.055	0.068	0.043	0.060	0.080		0.079
0.9	C_y(DL+LL)	0.037	0.025	0.052	0.040		0.070		0.062
0.85	C_x(DL+LL)	0.060	0.072	0.049	0.066	0.082		0.083
0.85	C_y(DL+LL)	0.031	0.021	0.046	0.034		0.065		0.057
0.8	C_x(DL+LL)	0.065	0.075	0.055	0.071	0.083		0.086
0.8	C_y(DL+LL)	0.027	0.017	0.041	0.029		0.061		0.051
0.75	C_x(DL+LL)	0.069	0.078	0.061	0.076	0.085		0.088
0.75	C_y(DL+LL)	0.022	0.014	0.036	0.024		0.056		0.044
0.7	C_x(DL+LL)	0.074	0.081	0.068	0.081	0.086		0.091
0.7	C_y(DL+LL)	0.017	0.011	0.029	0.019		0.050		0.038
0.65	C_x(DL+LL)	0.077	0.083	0.074	0.085	0.087		0.093
0.65	C_y(DL+LL)	0.014	0.008	0.024	0.015		0.043		0.031
0.6	C_x(DL+LL)	0.081	0.085	0.080	0.089	0.088		0.095
0.6	C_y(DL+LL)	0.010	0.006	0.018	0.011		0.035		0.024
0.55	C_x(DL+LL)	0.084	0.086	0.085	0.092	0.089		0.096
0.55	C_y(DL+LL)	0.007	0.005	0.014	0.008		0.028		0.019
0.5	C_x(DL+LL)	0.086	0.088	0.089	0.094	0.090		0.097
0.5	C_y(DL+LL)	0.006	0.003	0.010	0.006		0.022		0.014

Table:4 Negative moment coefficient for two-way slab

Calculation for the area of steel

Calculate R_u(in Mpa) for all positive and negative moments using the below formula:

Calculate steel ratio (ρ) using the below formula for each R_u

Calculate the Area of steel (in mm²/m) using the below formula for each ρ

Calculate the minimum area (in mm²/m) of steel.

Compare As with A_sminand select the greater value

Calculate the spacing of bars (in mm) using the governing value of each As

References:

All formulas are from “ACI 318 code”.
Moment coefficients for two-way slabs are taken from the book “Design of concrete structures by Winter/Nilson”.

Knowledge Sharing Platform

Designing Procedure of Slab through Moment Coefficient Method

Design Procedure of One-way Slab (Ly/L_x> 2)

Minimum thickness of slab

Loads on slab

Moment Calculation

Calculation for area of steel

Design Procedure of Two-way Slab (Ly /Lx < 2)

Minimum thickness of slab

Loads on slab

Moment Calculation

Negative(-ve) moment

Calculation for the area of steel

References:

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Designing Procedure of Slab through Moment Coefficient Method

Design Procedure of One-way Slab (Ly/Lx > 2)

Minimum thickness of slab

Loads on slab

Moment Calculation

Calculation for area of steel

Design Procedure of Two-way Slab (Ly /Lx < 2)

Minimum thickness of slab

Loads on slab

Moment Calculation

Negative(-ve) moment

Calculation for the area of steel

References:

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Design Procedure of One-way Slab (Ly/L_x> 2)