CONTINUOUS BEAM & ONE-WAY SLAB ANALYSIS - ACI 318 APPROXIMATE METHOD

Reference: ACI 318-19, Section 6.5

INPUT DATA

Beam Geometry

N = Number of equal spans (2 to 6)

L = ft Span length (clear span)

b = in Beam width

h = in Beam height (total depth)

Loads

w_D = kip/ft Unfactored dead load

w_L = kip/ft Unfactored live load

Figure 1: Geometry

Continous Beam or One-way Slab Analysis

Support Conditions

End Condition Types:

1: Discontinuous end unrestrained
2: Discontinuous end integral with support
3: Built integrally with spandrel beam
4: Built integrally with column

End Type = Select end condition

Column Stiffness Check (for option 4)

For beams built integrally with columns: If ΣK_col ≥ 8·ΣK_beam, use special coefficients

Stiff Ratio = ΣK_col/ΣK_beam (enter 0 if not applicable)

Deflection Parameters

f_c = ksi Concrete compressive strength

w_c = lb_f/ft³ Concrete unit weight

ξ = Time-dependent factor (default: 2.0 for 5+ years)

ρ_comp = Compression reinforcement ratio (0 if none)

APPLICABILITY CHECKS

ACI 318 approximate method requires specific conditions to be met

Check 1: Two or more spans ✓ OK

Check 2: Spans approximately equal (±20%) ✓ OK - Equal spans specified

Check 3: Uniformly distributed loads ✓ OK - Uniform loads specified

Check 4: Live load ≤ 3×Dead load

L/D ratio = w_L/w_D = 1.17

✓ OK

Check 5: Prismatic members ✓ OK - Prismatic section specified

Overall Applicability: METHOD IS APPLICABLE

LOAD COMBINATIONS

ACI 318-19, Section 5.3.1

w_u = 1.2×w_D + 1.6×w_L

w_u = 1.2×3.0 + 1.6×3.5 = 9.20 kip/ft

MOMENT AND SHEAR COEFFICIENTS

Based on ACI 318-19, Section 6.5, Table 6.5.2

Negative moment at exterior support: C_M,ext = 0

Negative moment at first interior support: C_M,int1 = 1/11

Positive moment in end span: C_M,pos1 = 1/11

Negative moment at interior supports: C_M,int = 1/11

Positive moment in interior spans: C_M,pos,int = 1/16

Shear coefficient at face of all supports: C_V = 0.575

DESIGN MOMENTS

Negative moment at exterior support: M_ext = C_M,ext×w_u×L²

M_ext = 0 = 0.00 kip·ft

Negative moment at first interior support: M_int1 = C_M,int1×w_u×L²

M_int1 = 0 = 0.00 kip·ft

Positive moment in end span: M_pos1 = C_M,pos1×w_u×L²

M_pos1 = 0 = 0.00 kip·ft

Negative moment at interior supports: M_int = C_M,int×w_u×L²

M_int = 0 = 0.00 kip·ft

Positive moment in interior spans: M_pos,int = C_M,pos,int×w_u×L²

M_pos,int = 0 = 0.00 kip·ft

Maximum design moment: M_max = 0.00 kip·ft

DESIGN SHEARS

Shear at face of all supports: V_u = C_V×w_u×L

V_u = 0 = 0.00 kip

DEFLECTION CALCULATIONS (Simplified)

Service Load Deflection

w_s = w_D + w_L = 3.0 + 3.5 = 6.50 kip/ft

Moment of inertia

I_g = b×h³/12

I_g = 10.0×20.0³/12 = 6666.67 in⁴

Modulus of elasticity (ACI 318-19, Section 19.2.2)

E_c = w_c^1.5 × 33 × √(f_c)

E_c = 155^1.5 × 33 × √(3) = 3372.82 psi

Maximum deflection for continuous beam (approximation)

For three or more spans:

Δ_max = w_s×L⁴/(145×E_c×I_g)

Δ_max = calculation = 0.000 in

Deflection limits (ACI 318-19, Table 24.2.2)

Δ_limit,live = L/360 = 19.6×12/360 = 0.653 in (For floors, L/360)

Δ_limit,total = L/240 = 19.6×12/240 = 0.980 in (For total load, L/240)

Immediate live load deflection (conservative estimate)

Δ_L = (w_L/w_s)×Δ_max

Δ_L = calculation = 0.000 in

Long-term deflection multiplier (ACI 318-19, Section 24.2.4)

λ_Δ = ξ/(1 + 50×ρ_comp)

λ_Δ = 2/(1 + 50×0) = 2.00

Additional long-term deflection

Δ_sustained = w_D×L⁴/(145×E_c×I_g)

Δ_sustained = calculation = 0.000 in

Δ_add = λ_Δ×Δ_sustained

Δ_add = calculation = 0.000 in

Total deflection

Δ_total = Δ_max + Δ_add

Δ_total = calculation = 0.000 in

Deflection Checks:

Live Load Deflection Check: ✓ OK (Δ_L = 0.00 ≤ Δ_limit,live = 0.00 in)

Total Deflection Check: ✓ OK (Δ_total = 0.00 ≤ Δ_limit,total = 0.00 in)

SUMMARY OF RESULTS

DESIGN MOMENTS:

Negative moment at exterior support: M_ext = 0.00 kip·ft

Negative moment at first interior: M_int1 = 0.00 kip·ft

Positive moment in end span: M_pos1 = 0.00 kip·ft

Negative moment at interior supports: M_int = 0.00 kip·ft

Positive moment in interior spans: M_pos,int = 0.00 kip·ft

Maximum design moment: M_max = 0.00 kip·ft

DESIGN SHEAR:

Shear at supports: V_u = 0.00 kip

DEFLECTION:

Gross moment of inertia: I_g = 0.00 in⁴

Modulus of elasticity: E_c = 0.00 ksi

Maximum immediate deflection: Δ_max = 0.00 in

Live load deflection: Δ_L = 0.00 in

Long-term multiplier: λ_Δ = 0.00

Additional long-term deflection: Δ_add = 0.00 in

Total deflection: Δ_total = 0.00 in

NOTES:

This analysis uses ACI 318 approximate coefficients
Moments are at face of support for negative moments
Clear span length (L) is used in calculations
Deflections are simplified estimates using gross section
For accurate deflection, use effective moment of inertia (I_e)
Consider moment redistribution if desired (up to 20%)
Column moments should be checked separately

RESULTS

METHOD IS APPLICABLE