Solution to Problem 446 | Relationship Between Load, Shear, and Moment

Problem 446
Beam loaded and supported as shown in Fig. P-446.
 

 
446-beam-supported-through-out.gif

 

Solution to Problem 445 | Relationship Between Load, Shear, and Moment

Problem 445
Beam carrying the loads shown in Fig. P-445.
 

 
445-simple-beam-uniform-and-trapezoidal-loads.gif

 

Solution to Problem 444 | Relationship Between Load, Shear, and Moment

Problem 444
Beam loaded as shown in Fig. P-444.

 
444-simple-beam-triangular-loads.gif

 

Solution to Problem 443 | Relationship Between Load, Shear, and Moment

Problem 443
Beam carrying the triangular loads shown in Fig. P-443.

 
443-simple-beam-triangular-load.gif

 

Solution to Problem 442 | Relationship Between Load, Shear, and Moment

Problem 442
Beam carrying the uniformly varying load shown in Fig. P-442.

 
442-simple-beam-triangular-load.gif

 

Floor Framing

In floor framing, the subfloor is supported by light beams called floor joists or simply joists which in turn supported by heavier beams called girders then girders pass the load to columns. Typically, joist act as simply supported beam carrying a uniform load of magnitude p over an area of sL, where
 

Economic Sections

From the flexure formula $f_b = My / I$, it can be seen that the bending stress at the neutral axis, where $y = 0$, is zero and increases linearly outwards. This means that for a rectangular or circular section a large portion of the cross section near the middle section is understressed.
 

For steel beams or composite beams, instead of adopting the rectangular shape, the area may be arranged so as to give more area on the outer fiber and maintaining the same overall depth, and saving a lot of weight.