7-5 provide a graphical solution for equations 7-13 (for fixed ended rectangular piers) and 7-14 (for

cantilever rectangular piers), respectively. When walls of different moduli of elasticity, Em, are being

compared, the deflection values shall be multiplied by the ratio of 1.35 x 106/Em. When walls of different

actual thicknesses or equivalent thicknesses, t, are being compared, the deflection values shall be multiplied

by the ratio of 12/t. In corner pier curves (1 and 3) the corner pier moment of inertia, I, is assumed to be 1.5

times that of the rectangular pier. The equations for the corner piers are derived by the procedure given above

(using equation 7-8 and 7-9) except that (1.5)I is substituted for I in the bending term of the equations, and

the correction factor of 1.2 in the shear term of the equations is replaced by 1.0, since the section can no

longer be considered rectangular. These substitutions result in equations 7-15 (for a fixed ended corner pier)

and equation 7-16 (for a cantilever corner pier) as follows:

For other values of I, the flexural portion of the deflection curves would be proportional. The deflections

shown on the charts are reasonably accurate. The formulas written on the curves can be used to check the

results. However, the charts will give no better results than the assumptions made in the shear wall analysis.

For instance, the point of contraflexure of a vertical pier may not be in the center of the pier height. In some

cases the point of contraflexure may be selected by judgment and an interpolation made between the

cantilever and fixed conditions.

of a shear wall section with one opening and give the complete design of a shear wall with two openings.

(1) Given:

f'm = 1350 psi

Em = l000f'm = 1,350,000 psi

Ev = 0.4Em = 540,000 psi.

(2) *Problem. *Determine the rigidity of the wall.

(3) *Solution. *The procedure involves determining the rigidities or stiffnesses of each segment within

the shear wall element. The method is based on the deflection charts of figure 7-5. In this method; the

deflection of the solid wall is determined, the deflection of the horizontal strip of the wall containing all the

openings is deducted from the solid wall deflection, and then the deflections of the piers within this opening

strip are added to this modified wall deflection to obtain the total deflection of the actual wall with openings.

The reciprocal of this deflection value becomes the relative rigidity of that wall. Note that the following

solution is carried out, in some instances, to four significant figures. This was done for calculation purposes

and does not imply that the deflections would actually be accurate to the degree of precision since the

procedure used is only approximate with simplified assumptions made.

rectangular pier cantilever curve #4 from figure 7-5). Note that the equivalent wall thickness for 12-inch

CMU with grouted cells @ 24" o.c. from table 5-2 is 5.7 inches.

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