Truss Analysis: Warren, Pratt, Howe and K Member Forces

About this Truss Analysis Calculator

This calculator builds a pin-jointed Warren, Pratt, Howe or K truss from a handful of inputs and solves every member force, the support reactions and the joint deflections, then checks the peak axial stress against yield. It is for:

• Structural engineers sizing the chords, diagonals and verticals of a roof girder, footbridge or lattice truss, who need the governing tension and compression members and the buckling length of the worst strut.
• Engineering students checking a method of joints or method of sections hand solution against an exact stiffness solution for the same geometry.
• Drafters and estimators comparing truss forms early in a job, when the question is which pattern puts the long members in tension and how the chord forces change with depth.

More info on Truss Analysis

How the truss is generated

Choose the type, span, depth and panel count and the page lays out the joints and members for you. A Warren truss has no verticals and its top chord joints sit between the bottom chord joints. Pratt and Howe trusses have verticals at every panel point, with the diagonals sloping the opposite way in each. The K truss splits each vertical at mid-height and runs two half-depth diagonals from that point. The joint load is applied to every interior joint of the chord you pick, top or bottom.

What the solution gives you

Tension is positive throughout. The page reports the reactions, the largest tension and compression in each member group, the governing compression member with its length, a count of zero-force members and the full force list by member name. The chart draws the truss with every member coloured by the sense of its force and weighted by magnitude.

Why forces do not depend on the section

A truss with a pin and a roller and a triangulated web is statically determinate, so the member forces follow from equilibrium alone. The section area and modulus you enter change only the deflection and the stress check, never the forces. That is why the output matches a hand calculation exactly.

From forces to member sizes

The stress check is against yield only. Every compression member also needs a buckling check on its own length, and that check usually governs the diagonals and the top chord. Carry the forces into a steel or timber member design page to finish the design.

Common Calculation Errors to Avoid

• Loading the support joints. A load placed directly over a bearing goes straight into the support without stressing the truss. Counting it as a joint load overstates the reactions and the end member forces.
• Mixing up the diagonal direction. Pratt and Howe trusses differ only in which way the diagonals slope, and that decides whether the long members are in tension or compression. Check the drawing before trusting the signs.
• Treating the yield check as the design. A slender diagonal buckles well before it yields. The peak stress utilisation is a screening check, not a member capacity.
• Using an odd panel count for a Pratt, Howe or K. The diagonals must mirror about mid-span. The page rounds an odd count up, so check the panel length it reports.

FAQs

Which truss members are in tension and which in compression?

Under gravity load on a simply supported truss, the top chord is in compression and the bottom chord in tension. In a Pratt truss the diagonals are in tension and the verticals in compression. In a Howe truss it is the reverse. In a Warren truss the diagonals alternate between tension and compression along the span. In a K truss the upper diagonal of each K is in compression and the lower one in tension.

Does the member area change the forces?

No. For a determinate truss the member forces follow from equilibrium and do not depend on the section. The area and modulus only affect the deflection and the stress check.

How do I check a method of joints hand calculation?

Enter the same span, depth, panel count and joint load, pick the same loaded chord, and read the force list. The member names use B for bottom chord joints, T for top chord joints and M for the mid-height joints of a K truss, numbered from the left support.

What does the zero-force member count mean?

Some members carry no force under the chosen load, usually the end posts or the centre vertical. They are still needed for stability and for other load cases, so do not remove them, but they do not need to be sized for this case.

Can I use this for a cantilever or a continuous truss?

Not directly. The page models a single span on a pin and a roller. A cantilever or a truss over several supports has a different support arrangement and, for a continuous truss, is statically indeterminate.