Note; As for the low roof area haunch properties Ix, Iy, Sx, and A as well as the length of the haunch were
previously calculated as; Ix = 640-in4 (266.4X106 mm4), Iy = 13.3-in4 (5.54X106 mm4), Sx = 58-in3
(950.4X103 mm3), A = 11.48-in2 (7.41X103 mm2), and ` ' length from centerline of column to toe of
haunch is 1.85'(22.25")(0.56m).
As in the case of the low roof, the moment frame was analyzed using a two-dimensional computer analysis
program (RISA-2D, version 4.0). All load combinations were investigated to determine the worst case
loading for each element and the worst case deflection for the frame. In all cases, the controlling load
combination was again equation 4a; 1.314D+QE+0.5L. After comparing the frame deflection to the
allowable story drift, a check on the strength requirements of the frame were completed. Since the same
members being used are the same as for the frame elements as at the low roof, a check to ensure the
location of the plastic hinge was determined to be unnecessary.
δalc = 0.565" (14.4mm)
(worst case at first
∆ allow = 0.025hsx
Allowable story drift;
∆ allow = 0.025(11' (12"/1' )) = 3.3" (83.8mm)
Cd xδalc = 5.5(0.565" ) = 3.11" < ∆ allow = 3.3" (79.0mm < 83.8mm)
The following maximum loads were obtained from the analysis output at the toe of the haunch;
M u,beam = 30.79 ft - kips , Vu,beam = 5.99 k (26.6KN)
φb M n = 109 ft - kips (147.8KN-m) per AISC LRFD 2nd ed. load factor design selection table (using an
unbraced length ` b'of the compression flange of 5' 1.53m))
φv Vn = 69 k (306.9KN)
per AISC LRFD 2nd ed. maximum uniform load tables
∴ M u,beam = 30.79 ft - kips < 109 ft - kips = φb M n (41.8KN-m < 147.8KN-m)
Vu,beam = 5.99 k < 69 k = φv Vn (26.6KN < 306.9KN)
Note: The columns will be analyzed as if it were a single story column spanning from the first floor level
to the roof and subjected to transverse loading (caused by the second floor diaphragm). Therefore, the
interstory drift in the moment magnification calculation will be taken as the displacement of the roof level
relative to the first floor level.
Per FEMA 302 paragraph 126.96.36.199.1, 30% of the seismic load effects from the orthogonal direction will be
included. Since in the orthogonal direction brace frames are acting, this results in only an additional axial
load. However, in this case the load resulting from the braced frames is zero.
Pu,total = 38.16k (169.7KN)