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which places in evidence the prominent role of cam function acceleration y on the vibrating system, similar to a system response to a shock input at its foundation The general solution to Eq (123) consists of the complementary or transient solution plus the particular solution The complementary solution is the solution to the homogenous equation mz + bz + kz = 0 2 z + 2zw n z + w n = 0 where w n = ( k m)



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If R1 r1 is initial radius of neutral axis, and R2 is nal radius, Net strain e under load is e Bending equation may be expressed as /y E (1/R2 1/R1) M/I (418b) (1/R2 1/R1) y (418a)

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496 Deep Beams with Small Initial Curvature (Non-linear Strain)

Figure 5-8

zc = Ae -zwnt sin[(1 - z 2 ) w n t ] + Be -zwnt cos[(1 - z 2 ) w n t ]

It is assumed that a neutral axis does not coincide with a geometric centroid The centroidal axis of a cross section is assumed at distance n from the neutral axis (Figure 410) If R1 is radius of curvature to neutral axis, R2 is radius of curvature to centroidal axis n R1 R2 R1 d/ [loge (R2 + d/2)/(R2 My nA (R1 + y ) 1/3 (d/2R2)2 1/5 (d/2R2)4 d/2)] (419a) (419b) ] (419c)

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Equation 418b may be expressed as [loge (R2 d/2)/(R2 d/2)]

(124)

These are the two views for adding new KPIs The top view creates a KPI in PerformancePoint based on cube measures The bottom view imports KPIs that are part of a cube in Analysis Services 2005

d/R2 [1

where A and B are determined in conjunction with the particular solution and the initial conditions One form of the particular solution is derivable from the impulse response zp = 1 (1 - z 2 )1 2 w n

A nonlinear equation will lead to non-linear stress distribution across the depth of a deep beam Currently this non-linear effect is being neglected by AASHTO for deep beams

(125)

bd3/12 (419d)

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For nite , the case here, zp(0) = zp(0) = 0, so that the general solution to Eq (123) is y -zw t z( 0) + z( 0)zw n 2 12 2 12 z = z p + 12 sin[(1 - z ) w n t ] + z( 0) cos[(1 - z ) w n t ] e n (126) (1 - z 2 ) w n where the initial conditions z(0) and z(0) are subsumed in zc Accordingly, for a system initially at rest, the zp solution becomes the complete solution However, the dif culty with this solution is that is periodic and integration would have to be performed y over many cycles depending on the amount of damping present Solutions would be analyzed rst to determine the input transient peak response, which is important in cam-follower system performance Incidentally, the steady-state response would be reached when z( nt ) = ( n + 1)T and z( nt ) = z( n + 1)T

The Targets column contains a drop-down list of all the measures in the cube, but the developer can also type in a hardcoded value if one exists Obviously, formulas can be placed in here as well, which will be discussed later The Adventure Works DW sample database is being used in the examples shown in the screenshots Two of the measures in the Adventure Works cube are called Sales Amount and Sales Amount Quota, and these two measures will work nicely as the Actual and Targets respectively Also, be aware that when the measures are changed, the Name field does not change, and therefore still contains the name of the first measure It s important that developers remember to change this before moving forward The next step in the process is to optionally add measure filters Measure filters are a way of selecting a member from a dimension that will limit what is seen in the value of the KPI and can be set for both the Actual and Target measures As an example, this KPI might be for a particular product line Therefore, selecting the checkbox to add measure filters allows the developer to choose a dimension

Actual shear stress xy Approximate shear stress It can be shown that:

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