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.

 
433-overhang-beam-point-and-moment-loads.gif

 

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

Problem 432
Beam loaded as shown in Fig. P-432.

 
432-overhang-beam-point-moment-and-uniform-loads.gif

 

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

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

 
431-overhang-beam-uniform-and-point-loads.gif

 

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

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

 
430-overhang-beam-uniform-and-point-loads.gif

 

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

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

 
429-overhang-beam-uniform-load.gif

 

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

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

 
428-overhang-beam-uniform-and-moment-loads.gif

 

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.

 
427-simple-beam-concentrated-and-uniform-load.gif

 

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.

 
426-cantilever-beam-uniform-and-moment-loads.gif

 

Solution to Problem 425 | Relationship Between Load, Shear, and Moment

Problem 425
Beam loaded as shown in Fig. P-425.

 
425-overhang-beam-concentrated-load.gif