It Ei

Here, for a single or double shear connection, nspj1 and n7 are the number of shear planes and the number of fasteners in a shear plane at end a, and nsp,2 and n2 are the number of shear planes and the number of fasteners in a shear plane at end b. K7 is the slip modulus of the connection at end a, and K2 is the slip modulus of the connection at end b, referred to in equation (12.41).

After solving (12.42) and (12.43) for M7 and M2 the equations can be written in terms of the rigidity factors:

M1 = ((4-—YY|Y2)) L (201 + Y202 — m(2(L — ai) — Y2ai)) (12.46) M2 ^(4—^) T (202 + Y101 + WL(2ai — Y1(L — ai))) (12.47)

The above are referred to as the modified slope equations and are simplifications of the more generalised format developed by Monforton and Wu that allow for relative lateral movement at the ends of each member. Those elements in the equations containing the free bending moment are the modified end fixing moments on the beam and can be written as

Table 12.4 The area of the free bending moment and the position of its centroid for typical load cases (see Figure 12.13 for symbols)
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