CE 101 - CONCRETE AND BEAM

Required Concrete Volume for a Slab

IN THEORY (Things that sounds simple enough)

Problem Statement : A reinforced concrete slab is to be constructed for a small storage area. The slab has the following dimensions:

Length = 5 meters, Width = 4 meters, Thickness = 0.15 meters

Determine the total volume of concrete required for the slab in cubic meters (m³)

Solution - The volume of concrete can be calculated using the simple formula for volume: V=L×W×T where:

VVV = Volume of concrete (m³), LLL = Length of slab (m), WWW = Width of slab (m), TTT = Thickness of slab (m)

Substituting the given values:

V=5×4×0.15, V=3.0 m³

Thus, the total concrete volume required is 3.0 cubic meters.

IN REALITY (things that many never considered - hence the abovementioned calculations will not really be accurate)

Wastage Factor

1) Some concrete is lost during mixing, transportation, and pouring.
2) (common practice) add 5-10% extra concrete for wastage.

Assuming 10% wastage, the adjusted volume is:
Vfinal​=3.0+(3.0×0.10)=3.3 m³

Risk Management

- Ensure proper formwork and leveling to prevent overuse or underuse of concrete.
- Consider site conditions, such as temperature, to prevent excessive shrinkage cracks.

So theory is not always compatible with reality.

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Determining the Maximum Load a Simply Supported Beam Can Carry

A simply supported reinforced concrete beam has the following properties:

Determine the maximum uniformly distributed load (𝑤) the beam can safely support, assuming a singly reinforced section and a safety factor of 1.5.

Determine the Moment Capacity (Mn) of the Beam

The nominal moment capacity of a singly reinforced beam is given by:

Substituting the given values:

First, simplify the fraction inside the parentheses:

Since 11.8 >1, it exceeds the valid range for this formula, meaning we need to check the compression-controlled section. However, for simplicity in this case, let's use a common approximate formula:

Apply the Safety Factor

Find the Maximum Uniform Load (w)

For a simply supported beam with a uniformly distributed load (w) the maximum moment occurs at mid-span and is given by:

The maximum uniformly distributed load the beam can safely carry is 0.56 kN/m.

Risk Management

Deflection Check - Ensure the beam does not deflect excessively under service loads.

Crack Control - Provide sufficient reinforcement to minimize cracks under bending stresses.

Concrete Quality - Ensure proper curing and material selection to achieve the intended strength.