Complex Diaphragms With Combined Openings and Offsets - The Analysis of Irregular Shaped Structures - page 321

Therefore the diagram closes.
Force diagrams at grid line 6, starting at grid line A:

( 303 61 . − 91 88 . )( + 261 62 . − 49 68 .

F A. =− () 10 =− 117 35 2 . lbcompression

2

2

( 261 62 . − 39 37 . )( + 135 63 . + 86 63 .

F B =− 2117 35 . − (30 ) =− 8785 lb compression

2

( 105 − 59 7 73 42

2

. )( . + − ) ()

F C =− 8785 + 35 =− 7199 5 .lb compression

( 521 92 . −+ 42 )( 584 92 . − 105 ) ()

F E =− 7199 5 . + 15 = 0 lb

2

Therefore the diagram closes.
Force diagrams at grid line 7, starting at grid line E:

584 92 . + 521 92 .

F C =− () 15 =− 8301 3 . lb tension

2

( 324 48 . − 87 3 .) ( + 177 48 . + 59 7 .) ()= 0lb

F B =− 8301 3 . + 35

2

Therefore the diagram closes.
Force diagrams at grid line 8, starting at grid line E:

158 16 . + 95 16 .

F C = () 15 = 1899 9 . lb compression

2

( 324 48 . − 270 2 .) ( + 177 48 . − 123 2 .) () = 0lb

F B = 1899 9 . − 35

2

Therefore the diagram closes.
Force diagrams at grid line 9, starting at grid line E:

F C =−1899 9 . lb tensionbyinspection ,

270 2 . + 123 2 .

F B =− 1899 9 . − () 35 =− 8784 4 . lb tens ion

2

( 135 63 . ++ 84 )( 303 61 . − 84 ) ()

F A =− 8784 4 . + 40 = 0 l b

2

Therefore the diagram closes.
All the force diagrams in the longitudinal and transverse directions close to zero;
therefore the analysis has been verified. ▲

This example demonstrates that designing minimal lateral-force-resisting systems
in the structure requires a significant increase in design time and detailing. It can also
be seen that establishing complete load paths in this diaphragm is difficult, especially
when alternative solutions are required once the consequences of the design are known.