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Solution to Problem 434 | Relationship Between Load, Shear, and Moment

Solution to Problem 433 | Relationship Between Load, Shear, and Moment

Problem 433
Overhang beam loaded by a force and a couple as shown in Fig. P-433.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Solution to Problem 432 | Relationship Between Load, Shear, and Moment

Solution to Problem 431 | Relationship Between Load, Shear, and Moment

Problem 431
Beam loaded as shown in Fig. P-431.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Solution to Problem 430 | Relationship Between Load, Shear, and Moment

Problem 430
Beam loaded as shown in Fig. P-430.

Click here to read or hide the general instruction

Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Solution to Problem 429 | Relationship Between Load, Shear, and Moment

Problem 429
Beam loaded as shown in Fig. P-429.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Solution to Problem 428 | Relationship Between Load, Shear, and Moment

Problem 428
Beam loaded as shown in Fig. P-428.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear.

Derivation of formula for volume of a frustum of pyramid/cone

Frustum of a pyramid and frustum of a cone

Frustum of a pyramid and frustum of a cone

The formula for frustum of a pyramid or frustum of a cone is given by

$V = \dfrac{h}{3} \left[ \, A_1 + A_2 + \sqrt{A_1A_2} \, \right]$

Where:
h = perpendicular distance between A₁ and A₂ (h is called the altitude of the frustum)
A₁ = area of the lower base
A₂ = area of the upper base
Note that A₁ and A₂ are parallel to each other.

Solution to Problem 427 | Relationship Between Load, Shear, and Moment

Problem 427
Beam loaded as shown in Fig. P-427.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear. (Note to instructor: Problems 403 to 420 may also be assigned for solution by semi-graphical method describes in this article.)

Solution to Problem 426 | Relationship Between Load, Shear, and Moment

Problem 426
Cantilever beam acted upon by a uniformly distributed load and a couple as shown in Fig. P-426.

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Without writing shear and moment equations, draw the shear and moment diagrams for the beams specified in the following problems. Give numerical values at all change of loading positions and at all points of zero shear. (Note to instructor: Problems 403 to 420 may also be assigned for solution by semi-graphical method describes in this article.)

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