In Broblem 14.66, assume that a uniform hoic 1 in. in diameter has been bored out of the center

step 1 In this question we have to tell that height up to which water will rise in capillary tube is gi

In Broblem 14.66, assume that a uniform hoic 1 in. in...

Key Concepts

Bending Stress

Bending stress is the internal stress induced in a material when an external bending moment is applied. It is typically calculated using the formula ? = M*c/I, where M is the applied moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the cross-sectional area. This concept is crucial for determining where the maximum stress occurs in any beam or shaft subject to bending loads.

Moment of Inertia

The moment of inertia is a geometric property of a cross-section that measures its resistance to bending. In the analysis of beams and shafts, it is used in the calculation of bending stresses and is determined by integrating the area distribution with respect to an axis. For composite sections, such as a shaft with a hole, the moment of inertia of the full section is reduced by subtracting the moment of inertia of the removed section.

Composite Section Analysis

Composite section analysis involves evaluating structures with non-uniform cross sections, where certain parts of the geometry are removed or added. In the context of a shaft with a central hole, the cross-sectional properties are adjusted by subtracting the contribution of the drilled-out area. This method is essential for accurately calculating the moment of inertia and overall stress distributions in modified or hollow sections.

Section Modulus

The section modulus is a geometric property that provides a direct measure for assessing the strength of a beam or shaft under bending loads. It is defined as the ratio of the moment of inertia to the maximum distance from the neutral axis (c). This value is used to calculate the maximum bending stress, with a higher section modulus indicating a more robust cross-section able to withstand larger moments with lower stress.

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