The stresses in all the truss members due to the unit load hung at
_J_ are readily found by the single diagram shown in Fig. 31, also
carefully drawn to scale. These stresses measured from the diagram
are given in the table as indicated by the column _z_; they are also
represented in equation (44) by the letter _z_. The quantity _s_ in
equation (44) is the intensity of the stress (pounds per square inch of
cross-section of member) produced by the combined dead and moving loads
in each member. As shown, these stresses are least in the web members
near the centre of the span, and greatest in the chord members. The
lengths in inches of the truss members are shown in the proper column
of the table. It will be observed that all counter web members are
omitted, as they are not needed for the uniform load. The coefficient
of elasticity (_E_) is taken at 28,000,000 pounds. The quantities
represented by the second member of equation (44) are computed from
these data, and they appear in the last column of the table, the sum
of which gives the desired deflection in inches. The elements of the
table show how much of the deflection is due to the chords and to the
web members, and they show that disregarding the latter would lead to a
considerable error.
+-------+----------+---------+--------+-----+---------+
| | _S_ | _s_ | _z_ | _l_ | _w_ |
+-------+----------+---------+--------+-----+---------+
| _L₁_ | +373,300 | +12,000 | +.555 | 360 | +.08563 |
| _L₂_ | +373,300 | +12,000 | +.555 | 360 | +.08563 |
| _L₃_ | +480,000 | +12,000 | +.833 | 360 | +.1284 |
| _L₄_ | +540,000 | +12,000 | +1.125 | 360 | +.1736 |
| _P₁_ | -502,300 | -9,000 | -.748 | 472 | +.1132 |
| _U₁_ | -501,000 | -9,500 | -.870 | 376 | +.1108 |
| _U₂_ | -544,800 | -10,000 | -1.135 | 363 | +.1472 |
| _U₃_ | -576,000 | -10,000 | -1.50 | 360 | +.1928 |
| _T₁_ | +84,000 | +9,000 | 0 | 324 | -- |
| _T₂_ | +143,500 | +10,000 | +.3738| 472 | +.0629 |
| _P₂_ | -12,000 | -1,000 | -.250 | 432 | +.00386 |
| _T₃_ | +93,720 | +7,400 | +.456 | 562 | +.0677 |
| _P₃_ | +12,000 | +1,000 | -.35 | 480 | -.0060 |
| _T₄_ | +60,000 | +4,800 | +.625 | 600 | +.0643 |
| _P₄_ | -12,000 | -1,000 | 0 | 480 | -- |
+-------+----------+---------+--------+-----+---------+
Deflection for ½ truss members = 1.2300 inches.
Deflection at _J_ = 2 × 1.2300 = 2.4600 inches.
[Illustration: FIG. 31.]
As the deflection is usually desired in inches, the lengths of members
must be taken in the same unit.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Elsewhere in the archive
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account