Trusses and Braced Systems

Trusses and Braced Systems

Use the current NCEES PE Civil Reference Handbook, AISC 15th Edition, and 2018 NDS/2015 SDPWS with ASD only for wood on the July 2026 exam. A truss diagram is an analytical model. It is powerful when its assumptions describe the structure and misleading when real load introduction, eccentric joints, or missing lateral restraint dominate.

State the idealization before solving

An ideal planar truss has straight members connected by frictionless pins at their centerline intersections. External loads and reactions act at joints, and each member is a two-force element carrying uniform axial tension or compression between joints. Under those assumptions, joint equilibrium or a section cut finds member forces without member bending.

Check the assumptions explicitly:

• Is a load applied at a panel point, or does it bear between joints on a chord?
• Do member work lines meet at one ideal joint?
• Is the truss planar, and what restrains movement out of its plane?
• Are supports represented by the correct reaction components?
• Does the selected joint or section have enough known forces for equilibrium?

A roof load delivered continuously through deck and purlins can bend the top chord between panel points even if the same load is converted to joint loads for global truss analysis. That conversion preserves global reactions and approximate axial action, but it does not erase local chord bending. Include self-weight and connection loads consistently.

Use tension-positive trial arrows in the method of joints. A negative answer identifies compression; it is not an algebra failure. Zero-force-member rules can simplify a determinate unloaded joint, but a member identified as zero for one load case may become active under wind reversal, unbalanced snow, erection loading, or a different support condition.

Worked support-joint calculation

A symmetric, simply supported 40-ft truss has a 20-kip downward joint load at midspan, so each vertical reaction is 10 kip. At the left support, a bottom chord is horizontal and a diagonal runs 10 ft horizontally and 8 ft upward to the next top joint. The diagonal length is

sqrt(10² + 8²) = 12.81 ft,

so sinθ = 8/12.81 = 0.6247 and cosθ = 10/12.81 = 0.7809. Assume member forces pull away from the joint. Vertical equilibrium gives

10 + Fd(0.6247) = 0,

therefore Fd = -16.0 kip: the diagonal is in compression. Horizontal equilibrium gives

Fbottom + (-16.0)(0.7809) = 0,

so Fbottom = +12.5 kip, tension. Joint equilibrium closes in both directions. Physically, the compressive diagonal supplies the downward component that balances the upward support reaction.

These are ideal axial forces. Suppose the diagonal's work line misses the connection work point by 2 in in the real gusset geometry. The local eccentric moment is approximately

Me = |Fd|e = 16.0(2) = 32 kip-in.

The gusset, welds or bolts, and connected chord must accommodate that effect under the applicable connection model. Calling the structure a truss does not make Pe vanish.

Concentric and eccentric braced frames

In a concentrically braced frame (CBF), brace, beam, and column work lines are arranged to intersect at a common work point under the system idealization, so braces resist lateral load primarily through axial force. Real gusset dimensions, connection stiffness, and unavoidable offsets still require the AISC model and detailing. Braces can see tension in one direction and compression in the reverse; compression strength and cyclic behavior are not inferred from tensile yielding.

An eccentrically braced frame (EBF) deliberately offsets a brace connection so a defined segment of the beam—the link—is subject to controlled shear and flexure and supplies inelastic deformation capacity under the AISC seismic provisions applicable to the selected system. An accidental 2-in connection offset in an ordinary truss does not make it an EBF. An EBF requires intentional system configuration, link analysis, bracing, connections, and capacity-based member design.

For either braced system, trace floor force through diaphragm collectors to the frame, then through brace, gusset, beam-column joints, columns, base plates, anchors, foundation, and soil. Chevron configurations can impose unbalanced vertical force on the beam when brace tension and compression responses differ. Do not design the braces while leaving the supporting beam out of equilibrium.

Out-of-plane stability and permanent bracing

A slender compression member can buckle about either axis. The planar truss drawing controls in-plane geometry but supplies no automatic out-of-plane restraint. Top-chord purlins, bottom-chord bracing, bridging, sheathing, and lateral restraint at joints must possess adequate stiffness and strength, connect at the assumed locations, and deliver bracing force to a stable diaphragm or braced bay. A line of braces connected only to other unstable members has no completed path.

Load reversal matters. A bottom chord in gravity tension may enter compression under uplift; a diagonal may switch sign; construction before deck attachment may have longer unbraced lengths than the completed structure. Wood truss plates, bolts, nails, steel gussets, welds, and member net sections must transfer the controlling forces without incompatible eccentricity or splitting. For wood, keep design and connection checks on the NDS ASD basis.

Exam workflow

Solve global reactions, validate the truss idealization, calculate axial forces, and then restore real-world effects: chord loading, eccentricity, connection geometry, buckling length, out-of-plane restraint, reversal, and foundation path. If the member-force diagram is correct but the compression chord can tip out of plane, the system is not correctly designed.