Analyses a truss in a vertical plane, with parallel chords, as a triangular roof truss or node by node: the member forces, reactions and node displacements, with pinned or rigid joints, self-weight, temperature, fabrication errors, the worst arrangement of the variable loads and influence lines of member forces. Every step shows its formula.

What it checks

Geometry: the overall length and height, the panel length a = l/n, the slope α of the first diagonal, and the numbers of nodes j and members m. The figure names the nodes B and T, the members TC, BC, D and V.
Determinacy: m + r − 2j, with r the reactions. At zero the truss is statically determinate: the forces follow from equilibrium alone, and temperature and fabrication errors only move the nodes. In an indeterminate truss (cross-braced, or pinned at both ends) they also produce forces.
Loads: the self-weight of the members G_m = γ·Σ A·l, the total vertical load as entered ΣF_y, and ΣF_y,var for the loads in the worst arrangement, all present.
Worst arrangement: a load on a chord or a group is present or absent member by member. All N_arr = 2ᵏ arrangements are covered, each load analysed once.
Reactions, member forces and node displacements, with the equilibrium check ΣR_y = ΣF_y. Tension is positive.
Deflection, optional: w_max ≤ l/n_lim, with w measured from the line through the supports.
Influence lines, optional: the force in up to four members for a unit load moving node to node along a chord, η_max and η_min with their positions, the areas A₊ and A₋, and N_max = P·η_max + q_m·A₊, N_min = P·η_min + q_m·A₋ under a moving force and a moving uniform load.

What you enter and what you get

You choose a truss with parallel chords (Pratt, Howe, Warren, Warren with verticals or cross-braced), a triangular roof truss with its apex at mid-span, or any truss node by node. For a regular truss: the span l, the depth h between the chord axes, the number of panels, support at the bottom or the top chord, and pinned at the left with a roller at the right, or pinned at both ends. Then E, pinned or rigid joints, and the area of each group: top chord, bottom chord, diagonals and verticals.

For the loads: whether they reach the truss at the nodes or along the members, the self-weight from a unit weight γ, up to six distributed loads, up to eight forces at nodes, up to four temperature changes and up to four members made too long or too short, each as entered or in the worst case. Then the deflection limit and the influence lines: the chord, the members, P and q_m.

You get the forces, reactions, displacements and influence lines, with a pass or fail for the deflection.

Assumptions and limits

Pinned joints: the ideal truss, axial force only. Rigid joints: the truss is solved as a frame and the members also bend; a second moment of area is then asked for every member.
At the nodes, each member's load goes half to each of its end nodes. Along the members, the chord also bends between the nodes.
Gussets and connections add 10 to 20 % to the weight: increase γ accordingly.
Linear analysis, except with tension-only members. Enter characteristic or design values as you need them.
Influence lines are straight between the nodes, and not available with tension-only members.
An analysis only: the members are not verified here.

Worked example

A Pratt truss of 24 m span and 2.5 m depth in eight panels, on the bottom chord, pinned at the left and on a roller at the right, with pinned joints, E = 210,000 N/mm² and areas of 6,000, 5,000, 3,000 and 2,500 mm² for the top chord, bottom chord, diagonals and verticals. Self-weight at 78.5 kN/m³, 12 kN/m on the top chord as entered, and in the worst arrangement 15 kN/m on the top chord and 40 kN at node B4; a limit of l/400; influence lines of BC4 and D1 for a load on the bottom chord, with P = 100 kN and q_m = 12 kN/m. The deflection check passes. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Description of the truss	Parallel chords
Pattern of the web	Pratt
Span between the supports l	24 m
Depth between the chord axes h	2.5 m
Number of panels n	8
Supported	At the ends of the bottom chord
Supports	Pinned at the left, roller at the right
Modulus of elasticity E	210000 N/mm²
Joints	Pinned — axial force only
Cross-section area A_TC	6000 mm²
Cross-section area A_BC	5000 mm²
Cross-section area A_D	3000 mm²
Cross-section area A_V	2500 mm²
Distributed loads and self-weight reach the truss	At the nodes — through purlins or cross-beams
Self-weight of the members	Included — from the areas and a unit weight
Unit weight of the material γ	78.5 kN/m³
Number of distributed loads	2
On	Top chord
Direction	Downward, per metre in plan
Intensity q₁	12 kN/m
Arrangement	As entered
On	Top chord
Direction	Downward, per metre in plan
Intensity q₂	15 kN/m
Arrangement	Worst case
Number of forces at nodes	1
At	B4
Horizontal force (to the right positive) F_x,1	0 kN
Vertical force (downward positive) F_y,1	40 kN
Arrangement	Worst case
Number of temperature changes	0
Number of members made too long or too short	0
Check the deflection against a limit	Yes
Limit: the span divided by n_lim	400
Influence lines of member forces	Yes
The load moves along	Bottom chord
Number of members	2
Member 1	BC4
Member 2	D1
Moving force P	100 kN
Moving uniform load q_m	12 kN/m

Calculation: The truss
Step	Value	Ref.
Overall length and height	B × H = 24.00 × 2.50 m
Panel lengtha = l/n	a = 3.000 m
Slope of the first diagonal	α = 39.8 °
Nodes and members	j / m = 18 / 33
Members and reactions against equations of the nodesm = 33 members, r = 3 reactions, j = 18 nodesstatically determinate: the forces follow from equilibrium alone; temperature and fabrication errors only move the nodes	m + r − 2j = 0

Calculation: The loads
Step	Value	Ref.
Self-weight of the membersγ·Σ A·l	G_m = 32.50 kN
Total vertical load as entereddownward positive	ΣF_y = 320.50 kN
Loads in the worst arrangement, all present	ΣF_y,var = 400.00 kN
The loads reach the trusseach member load half to each of its end nodes	at the nodes

Calculation: The worst arrangement
Step	Value	Ref.
Loads that may each be present or absentdistributed load 2 (member by member, 8 members), force at a node 1	k = 9
Arrangements coveredN_arr = 2ᵏeach load analysed once; the loads that increase a value are added for the largest result, those that decrease it for the smallest — the same as all 2ᵏ arrangements	N_arr = 512

Calculation: Support reactions
Step	Value	Ref.
Equilibrium: sum of the vertical reactionsequals ΣF_y = 320.50 kNa check of the analysis (loads as entered)	ΣR_y = 320.50 kN

Step	1B0pinned	9B8roller (left–right)
Horizontal reaction, from the loads as entered R_x kNto the right positive	0.00	·
largest R_x,max kN	0.00	·
smallest R_x,min kN	0.00	·
Vertical reaction, from the loads as entered R_y kNupward positive	160.25	160.25
largest R_y,max kN	360.25	360.25
smallest R_y,min kN	160.25	160.25

Calculation: Member forces
Step	Lengthm	N as enteredkN	N largestkN	N smallestkN
TC1T0 to T1	3.000	-168.0	-168.0	-381.0
TC2T1 to T2	3.000	-288.0	-288.0	-660.0
TC3T2 to T3	3.000	-360.0	-360.0	-837.0
TC4T3 to T4	3.000	-384.0	-384.0	-912.0
TC5T4 to T5	3.000	-384.0	-384.0	-912.0
TC6T5 to T6	3.000	-360.0	-360.0	-837.0
TC7T6 to T7	3.000	-288.0	-288.0	-660.0
TC8T7 to T8	3.000	-168.0	-168.0	-381.0
BC1B0 to B1	3.000	0.0	0.0	0.0
BC2B1 to B2	3.000	168.0	381.0	168.0
BC3B2 to B3	3.000	288.0	660.0	288.0
BC4B3 to B4	3.000	360.0	837.0	360.0
BC5B4 to B5	3.000	360.0	837.0	360.0
BC6B5 to B6	3.000	288.0	660.0	288.0
BC7B6 to B7	3.000	168.0	381.0	168.0
BC8B7 to B8	3.000	0.0	0.0	0.0
D1T0 to B1	3.905	218.7	496.0	218.7
D2T1 to B2	3.905	156.2	367.6	151.8
D3T2 to B3	3.905	93.7	248.0	76.2
D4T3 to B4	3.905	31.2	137.2	-8.3
D5B4 to T5	3.905	31.2	137.2	-8.3
D6B5 to T6	3.905	93.7	248.0	76.2
D7B6 to T7	3.905	156.2	367.6	151.8
D8B7 to T8	3.905	218.7	496.0	218.7
V1B0 to T0	2.500	-159.4	-159.4	-359.4
V2B1 to T1	2.500	-138.1	-138.1	-315.6
V3B2 to T2	2.500	-98.1	-95.3	-233.4
V4B3 to T3	2.500	-58.1	-46.9	-156.9
V5B4 to T4	2.500	-37.7	-37.7	-82.7
V6B5 to T5	2.500	-58.1	-46.9	-156.9
V7B6 to T6	2.500	-98.1	-95.3	-233.4
V8B7 to T7	2.500	-138.1	-138.1	-315.6
V9B8 to T8	2.500	-159.4	-159.4	-359.4

Calculation: Node displacements
Step	u_x largestmm	u_x smallestmm	w largestmm	w smallestmm
B0(0.00; 0.00)	0.00	0.00	0.00	0.00
B1(3.00; 0.00)	0.00	0.00	20.92	9.10
B2(6.00; 0.00)	1.09	0.48	37.96	16.44
B3(9.00; 0.00)	2.97	1.30	49.16	21.18
B4(12.00; 0.00)	5.37	2.33	53.40	22.85
B5(15.00; 0.00)	7.76	3.36	49.16	21.18
B6(18.00; 0.00)	9.64	4.18	37.96	16.44
B7(21.00; 0.00)	10.73	4.66	20.92	9.10
B8(24.00; 0.00)	10.73	4.66	0.00	0.00
T0(0.00; 2.50)	12.01	5.19	1.71	0.76
T1(3.00; 2.50)	11.10	4.79	22.43	9.76
T2(6.00; 2.50)	9.53	4.10	39.06	16.91
T3(9.00; 2.50)	7.54	3.25	49.85	21.46
T4(12.00; 2.50)	5.37	2.33	53.79	23.03
T5(15.00; 2.50)	3.19	1.42	49.85	21.46
T6(18.00; 2.50)	1.20	0.56	39.06	16.91
T7(21.00; 2.50)	0.04	-0.54	22.43	9.76
T8(24.00; 2.50)	-0.43	-1.37	1.71	0.76

Calculation: Check — deflection
Step	Value	Ref.
Largest deflection, at T4w_max ≤ l/n_lim	η = 0.897 · Pass90 % of the capacity used

Calculation: Influence lines
Step	Value	Ref.
The unit load moves alongstraight between the nodes: the load reaches the truss at the nodes	the bottom chord, 9 nodes

Step	1BC4B3–B4	2D1T0–B1
Largest ordinate η_max kN/kNthe force in the member for 1 kN at the node, tension positive	2.250	1.367
its position x mfrom the left end	9.00	3.00
Smallest ordinate η_min kN/kN	0.000	0.000
its position x m	0.00	0.00
Area of the positive part A₊ m∫ η dx where η > 0 (straight between the nodes)	27.000	16.402
Area of the negative part A₋ m	0.000	0.000
Largest force from the moving loads N_max kNP·η_max + q_m·A₊ (P = 100.0 kN, q_m = 12.0 kN/m)	549.0	333.5
Smallest force from the moving loads N_min kNP·η_min + q_m·A₋	0.0	0.0

How this module is verified

Verified against independent calculations used on real projects, before release.

Questions

Pratt or Howe?

In a Pratt truss the diagonals fall towards the middle and are in tension under gravity load, the verticals in compression. A Howe truss is the reverse.

Why are the influence lines straight between the nodes?

The moving load reaches the truss at the nodes, through cross-beams, as on a bridge or a crane runway.

Can I print the calculation?

The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.

Page updated: 14 November 2026

Plane truss analysis

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