Section modulus (Z) of a beam depends on

Explanation:

Section Modulus (Z) of a Beam

• The section modulus (denoted as Z) of a beam is a geometric property of the cross-section of the beam. It is a measure of the beam's strength, indicating its capacity to resist bending under a given load. The section modulus is defined as the ratio of the moment of inertia (I) of the cross-section about the neutral axis to the distance (y) from the neutral axis to the outermost fiber of the section:

Section Modulus Formula:

Z = \(\frac{I}{y}\)

• I: Moment of inertia of the cross-section about the neutral axis (measured in mm⁴ or in⁴).
• y: Distance from the neutral axis to the outermost fiber of the cross-section (measured in mm or in).

The section modulus is a critical parameter in the design of beams, as it helps engineers determine the bending stress a beam can safely withstand. A higher section modulus indicates a beam with greater bending strength.

Correct Option Analysis:

The correct option is:

Option 4: The geometry of the cross-section.

The section modulus (Z) is directly dependent on the geometry of the cross-section of the beam. This is because both the moment of inertia (I) and the distance to the outermost fiber (y) are determined by the shape and size of the cross-section. For example:

• A rectangular cross-section will have a different section modulus compared to a circular or I-shaped cross-section of the same material.
• For a given material, changing the dimensions of the cross-section (e.g., width and height for a rectangle or flange and web dimensions for an I-beam) will alter the moment of inertia and the distance to the outermost fiber, thereby affecting the section modulus.