## Example 324

Nodal Column Braces as Effective Continuous Braces

Consider a column of length 3Lb with two equally spaced nodal braces giving an unbraced length of Lb. Estimate the critical load of an ideally-braced column by approximating the nodal braces as an equivalent continuous brace.

Ideal nodal brace stiffness required to buckle between brace points (2\ „ Pcr 3Pcr n -4 - U -3 bi - - if

Equivalent continuous stiffness using Equation 32.13

"A

### 32.5.5 Lean-On Systems

Lean-on bracing systems provide a means for some members in a structural system to rely on other members for stability. One of the most commonly encountered examples of lean-on systems are frames with ''leaning'' pin-ended columns connected to columns with nonzero end restraint. For these systems, the Y1P concept [8] can be used to design the members. This concept states that a system remains stable so long as the sum of the applied loads, Y1P, is less than the sum of the buckling strength of each individual member, Y1 Pcr, and the load in any individual member is less than the load corresponding to buckling between braces (no sway) for that member. This concept is illustrated in Example 32.5.

EXAMPLE 32.5 Lean-On Column Brace

Is the W10 x 33 capable of bracing the W12 x 58? A36 steel, factored loads shown, fully braced out of plane

W10 x 33

50 k

W12 x 58

450 k

50 k

450 k

8 ft

8 ft

No sway capacity — From AISC Manual (KLy — 8 ft) W12 x 58: (fPn — 482 k) > (Pu — 450 k) OK

Sway capacity — Using Y1P concept

8 ft

8 ft

8 ft

Fy Ag

450 1

inelastic t = -7.38(0.735)log fPn = 0.85(0.342)(0.877) Column B (W10 x 33)

0 0