Beam Load The maximum load that can be safely supported by a...

Name: Problem 74, Chapter 1: Precalculus with Limits
Uploaded: 2021-02-23T23:23:17-08:00
Duration: 2 min 47 s
Channel: Ryan Pollard
Description: Beam Load The maximum load that can be safely supported by a horizontal beam varies jointly as the width of the beam and the square of its depth and inversely as the length of the beam. Determine the changes in the maximum safe load under the following conditions. (a) The width and length of the beam are doubled. (b) The width and depth of the beam are doubled.

Beam Load The maximum load that can be safely supported by a horizontal beam varies jointly as the width of the beam and the square of its depth and inversely as the length of the beam. Determine the changes in the maximum safe load under the following conditions. (a) The width and length of the beam are doubled. (b) The width and depth of the beam are doubled.

Beam Load The maximum load that can be safely
supported by a horizontal beam varies jointly as the
width of the beam and the square of its depth and
inversely as the length of the beam. Determine the
changes in the maximum safe load under the following
conditions.
(a) The width and length of the beam are doubled.
(b) The width and depth of the beam are doubled.

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Key Concepts

Joint Variation

Joint variation describes a situation where one variable is directly proportional to the product of two or more other variables. In the context of the beam load problem, this means that the maximum safe load is directly proportional to both the width of the beam and the square of its depth, so changes in these dimensions affect the load capacity multiplicatively.

Inverse Variation

Inverse variation occurs when one variable is proportional to the reciprocal of another. In this beam problem, the safe load is inversely proportional to the length of the beam, indicating that increasing the length of the beam will decrease its load capacity proportionally.

Scaling in Geometric Dimensions

Scaling in geometric relationships involves understanding how changes to dimensions affect the overall quantities when exponents are involved. For example, when the depth of the beam—which is squared in the formula—is doubled, the effect on the load capacity is more significant than a simple doubling, highlighting the importance of carefully considering exponent effects in proportional reasoning.

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