2.4.7 Quick Checks of Strength and Stiffness
Evaluation statements may require quick check estimates of the strength and stiffness of the building.
To check the average shear stress or drift for upper stories in addition to the first story, the story shear for an upper story may be approximated as follows:
j = number of story level under consideration.
n = total number of stories above ground level.
V = base shear from Equation 2-3.
Vj = maximum story shear at story Level j.
W = total seismic dead load.
Wj = total seismic dead load of all stories above Level j (see Section 2.4.1).
The following equation for the drift ratio is applicable only to regular, multistory, multibay frames with columns continuous top and bottom:
Cd = deflection amplification factor from Table 220.127.116.11.
DR = drift ratio = interstory displacement divided by interstory height.
E = modulus of elasticity (ksi).
h = story height (in.).
I = moment of inertia (in.4).
kb = I/L for the beam.
kc = I/h for the column.
L = center-to-center length (in.).
Vc = shear in the column (kips).
For reinforced concrete frames, use appropriate cracked section properties pursuant to ACI 318-95 or later. For other configurations of frames, compute the drift ratio from the principles of structural mechanics.
The equation for a quick estimate of the average shearing stress, (vavg), in the columns of concrete frames is as follows:
Ac = summation of the cross-sectional area of all columns in the story under consideration.
nc = total number of columns.
nf = total number of frames in the direction of loading.
Vj = story shear from Equation 2-11.
Equation 2-13 assumes that nearly all of the columns in the frame have similar stiffness. For other configurations of frames, compute the shear stress in the concrete columns from the principles of structural mechanics.
The equation for a quick estimate of the average wall shear stress (vavg) is as follows:
Aw = summation of the horizontal cross-sectional area of all shear walls in the direction of loading. The wall area shall be reduced by the area of any openings. For masonry walls, use the net area. For wood-framed walls, use the length rather than the area.
Vj = story shear at the level under consideration determined from Equation 2-11.
The allowable stresses for the various types of shear wall building are given in Section 5.1 for concrete shear walls, Section 5.3 for reinforced masonry shear walls, Section 5.4 for unreinforced masonry shear walls and Section 5.6 for wood shear walls.
The equation for a quick estimate of the average axial stress in the diagonal bracing (fbr) is as follows:
Abr = the average area of a diagonal brace (in.2).
Lbr = average length of the braces (ft).
Nbr = number of braces in tension and compression if the braces are designed for compression; if not, use the number of braces in tension, if the braces are not designed for compression.
s = average span length of braced spans (ft).
Vj = maximum story shear at each level (kips).