Every roof truss is a quiet lesson in balanced forces. Loads push down, members push and pull, and supports push back. This Simple Truss Calculator solves that balance for a basic king post truss. You enter the span, the centre height and two joint loads. The tool returns the support reactions and the force in each main member. Signs tell you whether members squeeze or stretch.
Understanding those forces explains why trusses use so little material. Triangular layouts turn bending loads into simple push and pull. That efficiency made trusses the backbone of modern roofing. The calculator above uses a simple statics model only. Real truss design needs an engineer, as explained below. First, the model itself is worth understanding properly.
What Is a King Post Truss?
A king post truss is the simplest traditional roof truss form. Two sloping top chords meet at a central top joint. A horizontal bottom chord ties the two wall tops together. One vertical member, the king post, hangs from the top joint. That post connects the ridge point to the bottom chord midpoint. Five joints and a handful of members complete the picture.
Symmetry makes this truss easy to analyse by hand. Both slopes share the same angle and length. Loads placed at the centre joints keep both halves balanced. Each support then carries exactly half of the total load. Asymmetric loads would need a longer method of joints analysis. This calculator deliberately stays with the symmetric teaching model.
Member names describe position, not the force they carry. Top chords form the sloping roof line itself. The bottom chord doubles as the ceiling tie in many buildings. The king post is the vertical centre member. Forces inside them change with span, height and loading. Naming them clearly prevents mix ups in results.
How the Truss Forces Are Found
Statics begins with the supports and overall balance. Total downward load equals the apex load plus the midspan load. Symmetry splits that total equally between the two supports. Each reaction therefore equals half of the combined load. No other external forces act in this simple model. That reaction value feeds every later member calculation.
The top chord force comes from the joint at the support. Vertical balance there involves the reaction and the chord force. The chord pushes at the chord angle, called theta here. Dividing the reaction by the sine of theta gives its size. The sign is negative, which signals compression in the member. Top chords in real roofs are indeed compression members.
Two members remain in this simple symmetric model. Bottom chord force equals the reaction divided by the tangent of theta. That value is positive, signalling tension along the ceiling line. King post force simply equals the midspan load itself. The vertical post carries that load straight up to the ridge joint. The largest absolute value among the three is also reported.
Compression and Tension in Plain Words
Compression means a member is being squeezed shorter. Think of pushing both ends of a ruler toward each other. Tension means a member is being stretched longer. Pulling a rope tight gives the everyday picture of tension. Truss signs capture this with a simple convention. Negative values mean compression, while positive values mean tension.
Different materials handle those two actions very differently. Timber and steel both resist compression well in short lengths. Long slender members, though, can buckle sideways under compression. Tension members cannot buckle, so they can be slimmer. Cables work in tension but never in compression. Matching material to force type is core truss craft.
Zero force members appear in larger truss layouts too. Geometry sometimes leaves a member carrying nothing under one loading. Such members still stabilise the frame under other loadings. They also brace longer members against buckling sideways. Beginners often find their emptiness surprising at first. The king post becomes one when the midspan load vanishes.
How to Use the Simple Truss Calculator
Collect the span, height and both joint loads first.
- Enter the truss span in feet
- Enter the centre height in feet
- Add the load at the top joint
- Add the load at the bottom middle joint
- Press Calculate to see all member forces
- Note the negative sign on the top chord
Worked Example 1: A Twenty Foot Garage Truss
The Inputs
Take a truss spanning 20 feet between its supports. Its centre height is 5 feet above the bottom chord. A load of 1,000 pounds acts at the top joint. Another 500 pounds hangs at the bottom middle joint. Both loads sit on the centre line, keeping symmetry.
The Calculation
Half the span is 10 feet, so theta is the arctangent of 5 over 10. That angle equals 26.6 degrees for both slopes. Total load is 1,500 pounds, so each reaction is 750 pounds. Top chord force equals minus 750 divided by sine of theta. Bottom chord force equals 750 divided by the tangent.
The Result
The top chord force comes out at minus 1,677.05 pounds. That negative value means the top chords are in compression. Bottom chord force is 1,500.00 pounds of tension. King post force equals 500.00 pounds, the midspan load itself. The largest member force is therefore 1,677.05 pounds.
Worked Example 2: A Thirty Foot Barn Truss
The Inputs
Now scale up to a barn truss spanning 30 feet. Centre height rises to 10 feet above the chord. The top joint carries 3,000 pounds of load. The bottom middle joint carries 1,000 pounds. Total load across the truss is 4,000 pounds.
The Calculation
Half the span is 15 feet, so theta is the arctangent of 10 over 15. That angle equals 33.7 degrees this time. Each reaction equals half of 4,000, or 2,000 pounds. Top chord force equals minus 2,000 divided by the sine of theta. Bottom chord force equals 2,000 divided by the tangent.
The Result
The top chord force reaches minus 3,605.55 pounds of compression. Bottom chord force is exactly 3,000.00 pounds of tension. King post force equals 1,000.00 pounds of tension. The largest member force is 3,605.55 pounds in the top chords. Steeper angles reduced forces compared with a flatter roof.
Why Truss Height Changes Everything
Height controls the chord angle, and angle controls force size. Shallow trusses force members to work much harder. Their chords carry huge forces for modest roof loads. Steeper trusses convert loads into member forces more gently. The reaction divides by a larger sine value. That is why flat trusses need such beefy chords.
Designers balance height against building practicalities every day. Taller trusses create more attic space and steeper roofs. They also need longer members and higher gable walls. Transport limits cap the height of factory made trusses. Site built trusses dodge transport limits but cost more labour. Geometry, budget and logistics all meet at height.
What This Model Leaves Out
Real roofs spread loads across many joints, not two. Snow drifts, wind uplift and ceiling weight act together. Members also carry their own weight in real designs. Connections, plates and bearings need their own careful checks. Buckling rules govern slender compression members in codes. None of that fits inside a simple statics model.
Those omissions are exactly why engineers design real trusses. This calculator is a statics model for a simple truss only. Use it for learning, estimating and early comparisons. Never size structural members for a real building from it. Licensed engineers and truss manufacturers carry that responsibility. Their software models every load case in detail.
How Engineers Go Further
Professional analysis starts with the method of joints idea here. Engineers then add distributed loads across all panel points. Computer models test dozens of load combinations automatically. Timber grades, plate sizes and deflection limits follow. Wind uplift can even reverse some member forces. Designs must survive every credible combination safely.
Codes also demand checks that hand methods rarely touch. Bearing stress where trusses rest on walls matters. Lateral bracing keeps compression chords from buckling sideways. Ceiling drywall can crack if deflection runs too high. Each check protects a different failure mode. Thoroughness, not one big calculation, creates safe roofs.
Deflection limits protect finishes as much as strength does. A truss can be strong yet bend too much for ceilings. Engineers therefore check sag under full service loads. Long spans make deflection the governing design question. Stiffer chords and deeper truss profiles reduce sag. Comfort and appearance ride on those quiet checks.
Reading the Signs Correctly
Sign errors cause the most confusion for truss beginners. A negative top chord value is expected and healthy. It confirms the chord is pushing, as designed. A positive bottom chord value likewise confirms healthy tension. Trouble would be signs appearing opposite to these patterns. Such surprises usually mean an input was entered wrongly.
King post force sometimes puzzles learners as well. It equals the midspan load exactly in this model. With no midspan load, the king post carries nothing here. Real ceiling loads would load it in practice. That gap shows the teaching nature of the model clearly. Enjoy the clarity, but respect its limits.
Trusses in Everyday Buildings
Garages and barns display king post geometry openly. Exposed timber trusses decorate many converted barns and halls. The central post and sloping chords are easy to spot. Roof loads in such buildings follow the paths described here. Even hidden factory trusses obey the same statics. Only their web layouts grow more complex.
Historic buildings preserve much larger king post examples. Medieval halls spanned impressive widths with oak members. Iron straps reinforced joints where timber alone was weak. Many of those roofs still perform after centuries. Their survival teaches respect for sound geometry. Modern analysis simply quantifies what craftsmen intuited.
Metal connector plates changed how trusses get built today. Toothed plates press into timber at every factory joint. They replaced many bolts, straps and hand cut joints. Historic trusses relied on pegs and mortise joints instead. Both systems chase the same goal of reliable joints. Force paths, however, remain identical across the centuries.
Tips for Learning Truss Statics
These habits make force results easier to trust and learn from.
- Sketch the truss and label every joint first
- Check that both reactions sum to total load
- Expect compression in the sloping top chords
- Expect tension along the bottom chord always
- Try doubling the height and compare forces
- Watch how shallow angles inflate member forces
- Keep load units consistent across every input
- Let engineers design any truss you actually build
Frequently Asked Questions
General Questions
1. What does this Simple Truss Calculator solve?
It solves support reactions and member forces for a king post truss. Inputs are span, centre height and two joint loads. Outputs include the chord angle and the largest member force. Signs show compression or tension in each member.
2. Why is the top chord force negative?
Negative values signal compression under the sign convention used here. Top chords are squeezed by the roof loads above them. The size matters more than the sign for comparisons. Always report it as compression, not negative tension.
3. What does the king post do?
The king post links the ridge joint to the bottom chord midpoint. In this model it carries the midspan load in tension. It also helps support the bottom chord centre. Real king posts may carry ceiling loads as well. Its force here equals the middle load exactly.
4. Can I design a real roof truss with this?
No, real truss design requires a qualified engineer. This model omits distributed loads, wind and member weight. Codes demand many further checks on real structures. Use the results for learning and rough comparisons only.
5. Which loads belong at the two centre joints?
The top joint load represents forces delivered at the ridge point. The middle load represents forces hanging at the bottom chord centre. Real roof loads spread across many joints instead. Keep both loads on the centre line for symmetry.
How the Calculation Works
6. How are the support reactions found?
Total load equals the apex load plus the midspan load. Symmetry splits that total equally between both supports. Each reaction is therefore half of the combined load. Vertical balance for the whole truss is satisfied exactly.
7. How is the top chord force calculated?
The reaction is divided by the sine of the chord angle. A negative sign is attached to show compression. Steeper angles produce smaller top chord forces. Shallower angles make that force grow quickly.
8. How is the bottom chord force calculated?
The reaction is divided by the tangent of the chord angle. The result is positive, showing tension in the chord. That tension ties the wall tops against spreading. Bottom chords in real trusses indeed work in tension. Its size falls as the truss grows taller.
9. Why does the king post force equal the midspan load?
Vertical balance at the bottom middle joint explains it. Only the king post can pull upward at that joint. It must therefore carry the full downward load applied there. No other member at that joint has a vertical part. The equality is exact within this model.
10. How is the chord angle found?
The angle uses the arctangent of height over half span. Height is measured to the centre top joint. Half span is the horizontal distance to that joint. The result is converted into degrees for display. Both slopes share this same angle by symmetry.
Practical Questions
11. What happens to forces when the truss is flatter?
Member forces rise sharply as the angle shrinks. Dividing by a small sine value inflates the top chord force. Bottom chord tension grows by the same logic. Very flat trusses need much stronger members. Height is the cheapest force reducer available.
12. What if I enter zero for both loads?
The calculator asks for at least one positive load. Zero total load would make every force zero anyway. That result teaches nothing and signals an input slip. Enter the apex load, the midspan load, or both. Negative loads are also rejected as invalid.
13. Does the model handle loads placed off centre?
No, off centre loads break the symmetry this model assumes. Reactions would differ between the two supports then. A full method of joints analysis handles such cases. Engineers use software for asymmetric real world loading. Keep loads centred when using this tool.
14. Which member usually carries the largest force?
The top chord usually carries the largest absolute force. Its value combines the reaction with a shallow angle effect. The calculator reports the maximum across all three members. In both worked examples the top chord governed. Checking the maximum guides any rough comparison.
15. What units does the calculator use?
Span and height are entered in feet. Loads and forces are expressed in pounds. Angles appear in degrees to one decimal place. Forces show two decimal places for clarity. Keep every input in those units consistently.
CONCLUSION
Simple statics reveals the hidden push and pull inside a truss. This Simple Truss Calculator finds reactions, chord forces and the king post force. Negative top chord values correctly show compression at work. Use the model to learn and compare shapes freely. Then leave real structural design to qualified engineers.