Bending Strength of a Beam Word Problems Fun Math Game Tips:
- A '2 by 6' stick of lumber can be more than twice as strong as a '2 by 4' of the same material length,
when the 'depth = 6' is kept vertical and the stick length is horizontal with support at each end.
- Experiments show that the vertical strength of a horizontal beam varies as the square of its depth.
Since the value of 62 = 36 is more than double the value of 42 = 16,
then a '2 by 6' stick of lumber is more than twice as strong as a '2 by 4'.
- Experiments on timber beams with a rectangular cross-section of 'breadth = b' and 'depth = d'
also show that a beam's loading strength varies directly as its breadth.
Generally speaking, a beam's bending strength S depends on the formula bd2.
- A beam with b=2 cm and d=3 cm is stronger than a beam with b=3 cm and d=2 cm
when they have the same material length, since bd2=(2)(32)=18 is larger than bd2=(3)(22)=12.
- This game assumes all the rectangular beams have the same horizontal length
and are supported beneath their ends with the bending load strength measured mid-length.
- Other experiments for Load = S include the beam length = L and a material constant = K
to yield a more detailed formula for bending strength S = K(bd2)/(L).
- Engineers use Strength formulas to establish the safe size of beams for community Building Codes.
This ensures safe floor joists, door and window headers, roof trusses and bridge components.
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