Preliminary Design Loads & Structural Material Properties

Contents

1. Classification of Structural Loads
2. Load Provisions under BNBC 2020
3. Concrete: Strength & Modulus of Elasticity
4. Reinforcement: Grades & Standards
5. Minimum Thickness of Slabs
6. Monolithic & Composite Concrete Beams
7. Worked Example: Minimum Slab Thickness
8. References

Before a single member can be sized, a designer must first agree on what the structure must resist and what it is made of. This note collects the preliminary information a reinforced-concrete designer reaches for again and again — load classification, code-based load values, concrete and steel material properties, and the empirical slab-thickness limits used to control deflection — closing with a complete worked example that ties the provisions together.

01Classification of Structural Loads

Every structural design begins with a preliminary inventory of the loads a building must carry. These are conventionally grouped into four categories:

Category 01

Dead Load

• Self-weight
• Floor finish
• Partition wall
• Wall load
• Others

Category 02

Live Load

• Occupancy-based, transient loading

Category 03

Lateral Load

• Wind load
• Earthquake load

Category 04

Snow Load

• Applicable to snow-prone regions

Dead load comprises everything permanently attached to the structure, namely:

• The self-weight of structural members
• Floor finishes
• Partition and wall loads
• Other fixed elements

Lateral load, by contrast, arises from environmental actions acting horizontally on the structure, principally wind load and earthquake (seismic) load.

Fig. A. The structural load path — gravity loads (dead and live) are applied to the slab, distributed to beams, carried down through columns, and finally transferred by the foundation to the soil.

02Load Provisions under BNBC 2020

Dead load and live load values for design are prescribed in the Bangladesh National Building Code.

DL & LL INFO [BNBC‑2020]
PART 6  ›  CHAPTER 2  ›  TABLE 6.2.1, 6.2.2, 6.2.3

These tables set out the minimum dead and live load intensities to be adopted for the elements and occupancy types covered by Chapter 2 of Part 6, and form the starting point for any gravity-load takedown on a reinforced-concrete structure designed to Bangladeshi practice.

Minimum Concrete Strength

The minimum specified concrete compressive strength is 20 N/mm², reducing to 17 N/mm² for buildings of up to four storeys.

03Concrete: Strength & Modulus of Elasticity

Modulus of Elasticity

Definition

The modulus of elasticity is the ratio of normal stress to the corresponding strain, for tensile or compressive stresses below the proportional limit of the material.

The ACI Code provides two permissible expressions for the modulus of elasticity of concrete, E_c, depending on the density of the concrete used.

Fig. 1. ACI Code Section 19.2.2.1 — permissible expressions for the modulus of elasticity, Eₛcₜ, of concrete.

Brick Aggregate Concrete

$$E_c = 3750\sqrt{f'_c}\ \ (\text{MPa})$$

An equivalent, customary-unit formulation appears in design texts as well, applicable to concretes weighing between 90 and 155 lb/ft³, together with the ACI simplified expression for normal-weight concrete at approximately 145 lb/ft³:

Modulus of Elasticity — Customary Units

$$E_c = w_c^{1.5}\,33\sqrt{f'_c}$$

In this expression, E_c is the modulus of elasticity in psi, w_c is the weight of the concrete in pounds per cubic foot, and f′_c is its specified 28-day compressive strength in psi. This is actually a secant modulus with the line (whose slope equals the modulus) drawn from the origin to a point on the stress–strain curve corresponding approximately to the stress (0.45 f′_c) that would occur under the estimated dead and live loads the structure must support.

For normal-weight concrete weighing approximately 145 lb/ft³, the ACI Code states that the following simplified version of the previous expression may be used to determine the modulus:

$$E_c = 57{,}000\sqrt{f'_c}$$

Lightweight vs. Normal-Weight Concrete

Lightweight concrete is defined as concrete containing lightweight aggregate and having an equilibrium density — as determined by ASTM C567 — between 1440 and 2160 kg/m³. The associated lightweight modification factor, λ, is given in Part 6, Chapter 6, Section 6.1.9 of the code:

Fig. 3. Lightweight factor, λ, per BNBC 2020 Part 6, Chapter 6, Section 6.1.9.

Fig. 3a. ACI Table 19.2.4.1(a) — values of λ for lightweight concrete based on equilibrium density.

Fig. 3b. ACI Table 19.2.4.1(b) — values of λ for lightweight concrete based on composition of aggregates.

ACI 19.2.4.2 & 19.2.4.3

19.2.4.2 It shall be permitted to take λ as 0.75 for lightweight concrete.

19.2.4.3 The value of λ shall be taken as 1.0 for normalweight concrete.

Normal-weight concrete contains only coarse and fine aggregates conforming to ASTM C33, with a density greater than 2160 kg/m³. In practice, normal-weight concrete typically falls between 2160 and 2560 kg/m³, and is conventionally taken as 2320 to 2400 kg/m³ for design purposes.

Specified Compressive Strength

The ACI Code sets minimum values of specified compressive strength, f′_c, according to the application and the seismic design category (SDC) governing the structure.

Fig. 3c. ACI Table 19.2.1.1 — limits for f′_c.

Footnote

For design of special moment frames and special structural walls used to resist earthquake forces, the Code limits the maximum f′_c of lightweight concrete to 5000 psi. This limit is imposed primarily because of a paucity of experimental and field data on the behavior of members made with lightweight concrete subjected to displacement reversals in the nonlinear range.

04Reinforcement: Grades & Standards

Two reinforcing steel grades are generally referenced in preliminary design:

• Grade 60
• Grade 72

ASTM A615

Deformed and plain carbon-steel bars for concrete reinforcement are designated under ASTM A615. The standard's Table A1.1 tabulates nominal weight, nominal dimensions (diameter, cross-sectional area, and perimeter), and deformation requirements for each bar size, from the No. 10 bar through the No. 60 bar.

Fig. 4. ASTM A615 Table A1.1 — deformed bar designations, nominal weights, dimensions, and deformation requirements.

FEMA 356

Where an existing structure's steel properties must be translated from lower-bound to expected-strength values — as is common in seismic evaluation and retrofit work — FEMA 356 provides tabulated multiplying factors organized by property (tensile or yield strength), construction era, and governing ASTM specification.

Fig. 5. FEMA 356 Table 5-3 — factors to translate lower-bound steel properties to expected-strength steel properties.

05Minimum Thickness of Slabs

The ACI Code limits slab thickness empirically to control deflection without requiring an explicit deflection calculation, provided the applicable limitations are satisfied. Three slab configurations are covered.

5.1  One-Way Slabs

For solid, nonprestressed one-way slabs, the minimum overall thickness, h, depends only on the support condition and the clear span, ℓ:

Fig. 6. ACI Table 7.3.1.1 — minimum thickness of solid nonprestressed one-way slabs.

These expressions apply to normal-weight concrete with f_y = 60,000 psi. Where conditions depart from this baseline, the following modifiers apply:

Fig. 7. ACI Sections 7.3.1.1.1–7.3.1.1.3 — modifiers for fₛyₜ other than 60,000 psi and for lightweight and composite slabs.

5.2  Two-Way Slabs Without Interior Beams

For nonprestressed slabs without interior beams spanning between supports on all sides, having a maximum ratio of long-to-short span of 2, overall slab thickness h shall not be less than the limits in Table 8.3.1.1, and shall be at least the value in (a) or (b) below, unless the calculated deflection limits of 8.3.2 (ACI 318) are satisfied:

• (a) Slabs without drop panels … 5 in.
• (b) Slabs with drop panels … 4 in.

For f_y exceeding 80,000 psi, 8.3.2 (ACI 318) shall be satisfied.

Beyond these absolute minimums, minimum thickness is governed by yield strength, panel location, and the presence of drop panels and edge beams:

Fig. 8. ACI Table 8.3.1.1 — minimum thickness of nonprestressed two-way slabs without interior beams.

Drop Panel

A drop panel in a nonprestressed slab, where used to reduce the minimum required thickness in accordance with 8.3.1.1 [The information beginning in Section 5.2] or the quantity of deformed negative moment reinforcement at a support in accordance with 8.5.2.2, shall satisfy (a) and (b):

• (a) The drop panel shall project below the slab at least one-fourth of the adjacent slab thickness.
• (b) The drop panel shall extend in each direction from the centerline of support a distance not less than one-sixth the span length measured from center-to-center of supports in that direction.

Section 8.5.2.2 (ACI -318) stated as: In calculating M_n for nonprestressed slabs with a drop panel, the thickness of the drop panel below the slab shall not be assumed to be greater than one-fourth the distance from the edge of drop panel to the face of column or column capital.

5.3  Two-Way Slabs With Beams on All Sides

Where beams span between supports on all sides of a panel, the minimum thickness depends on α_fm, the average flexural stiffness ratio of the edge beams, with three regimes defined below.

Fig. 9. ACI Table 8.3.1.2 — minimum thickness of nonprestressed two-way slabs with beams spanning between supports on all sides.

06Monolithic & Composite Concrete Beams

When a slab is cast integrally with its supporting beam, the slab acts compositely with the beam as a flange, and an effective overhanging flange width, b_e, must be established for both interior (T-beam) and edge (L-beam) conditions.

Fig. 10. Effective flange width and overhang limits for monolithic or composite concrete beams acting with the slab as a flange.

The governing limits, expressed above, cap the effective flange projection on each side of the web at eight times the flange thickness for interior beams (and correspondingly for edge beams), while the beam overhang h_b extending beyond the flange is limited relative to the flange thickness, h_f, and web width, b_w.

07Worked Example: Minimum Slab Thickness

The following example applies the two-way slab provisions of Sections 5.2–5.3 to a complete floor panel, following the ACI Code's minimum-thickness-to-control-deflection procedure.

Design Example

Minimum Thickness of an Interior Two-Way Slab Panel

Given: A floor system consisting of solid slabs and beams spanning in two directions, supported on 20″ × 20″ columns, 12 ft long. Using the ACI Code equations, determine the minimum slab thickness required for an interior panel. Use f′_c = 3 ksi and f_y = 60 ksi.

Fig. 13. Floor plan, interior panel section, beam section (B-B), and T-section geometry for the worked example.

Governing Deflection-Control Provisions (ACI 9.5.3)

Because two-way slab deflections are complex to compute directly, the ACI Code instead limits slab thickness through three empirical cases, based on α_fm, the average value of α_f for the beams enclosing the panel:

Fig. 11. Minimum slab thickness to control deflection (ACI 9.5.3) — Equations 17.1–17.3.

Fig. 12. Definitions of αₛfmₜ, αₛfₜ (Eq. 17.4), and the absolute minimum thickness limits.

1Set Up the Governing Equation

Equation 17.1 requires α_fm to be determined first, which in turn requires I_b, I_s, and α_f for the beams and slab in both the long and short directions.

2Gross Moment of Inertia of the Beam, I_b

The beam section is taken together with the slab extension on each side, limited to x = y but not more than four times the slab thickness. Assuming h = 7 in. (to be checked later), x = y = 22 − 7 = 15 in. < 4 × 7 = 28 in., so the full 15 in. governs and b_e = 16 + 2(15) = 46 in., producing the T-section shown above.

Taking moments about the top of the flange to locate the centroid:

• Area of flange = 7 × 46 = 322 in.²
• Area of web = 16 × 15 = 240 in.²
• Total area = 562 in.²

(322 × 3.5) + (240 × (7 + 7.5)) = 562 y  ⇒  y = 8.20 in.

$$I_b=\left[\frac{46}{12}(7)^3+322\times(4.7)^2\right]+\left[\frac{16(15)^3}{12}+240(7.5-1.2)^2\right]=22{,}453\ \text{in.}^4$$

3Slab Moment of Inertia (Long Direction)

With b = 20 ft and h = 7 in.:

$$I_l=\frac{(20\times12)(7)^3}{12}=6860\ \text{in.}^4 \qquad \alpha_{f1}(long)=\frac{EI_b}{EI_s}=\frac{22{,}453}{6860}=3.27$$

4 Slab Moment of Inertia (Short Direction)

With b = 24 ft and h = 7 in.:

$$I_s=\frac{(24\times12)(7)^3}{12}=8232\ \text{in.}^4 \qquad \alpha_s (short)=\frac{EI_b}{EI_s}=\frac{22{,}453}{8232}=2.27$$

5Average

$$\alpha_{fm} (average)=\frac{3.27+2.72}{2}=3.0$$

6Ratio of the long to the short Clear Spans

$$\beta=\frac{\left(24-\tfrac{20}{12}\right)}{\left(20-\tfrac{20}{12}\right)}=\frac{22.33}{18.33}=1.22$$

7Determine h_min from Equation 17.1 (ℓ_n = 22.33 ft)

$$h_{min}=\frac{(22.33\times12)(0.8+0.005\times60)}{36+(5\times1.22)[3.0-0.2]}=5.57\ \text{in.}$$

8Check Against Equation 17.2 (alpha_fm > 2.0)

The computed thickness must not fall below the value given by Equation 17.2:

$$h=\frac{294.8}{36+9(1.22)}=6.27\ \text{in.}$$

Result

Since the absolute minimum of 3.5 in. is not controlling, Equation 17.2 governs and h = 6.27 in. In practice, a slab thickness of 6.5 in. or 7.0 in. would be adopted. Note that in most practical cases, Equation 17.2 is the controlling condition.

 References & Governing Codes

1. Bangladesh National Building Code (BNBC), 2020 — Part 6, Chapter 2, Tables 6.2.1–6.2.3 (loads); Part 6, Chapter 6, Section 6.1.9 (lightweight factor, λ).
2. ACI 318 Building Code Requirements for Structural Concrete — Sections 19.2.2.1 (modulus of elasticity), 7.3.1.1 (one-way slab thickness), 8.3.1.1–8.3.1.2 (two-way slab thickness), 9.5.3 (deflection control).
3. ASTM C33 — Standard Specification for Concrete Aggregates.
4. ASTM C567 — Standard Test Method for Determining Density of Structural Lightweight Concrete.
5. ASTM A615 — Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement.
6. FEMA 356 — Prestandard and Commentary for the Seismic Rehabilitation of Buildings.