SkyCiv Truss Tutorial: Analyze Structures Step by Step

A truss is a structural component where moment value is zero, and members only carry axial forces (tensile or compressive). Members connect through pin joints ensuring zero moment at joints. All external loads must be applied at joints; loads on members convert the structure to a frame. Members are slender (length >> cross-sectional dimensions) and must be straight. The degree of static determinacy is Ds = m + r - 2j: Ds = 0 indicates perfect truss, Ds > 0 indicates redundant truss, Ds < 0 indicates unstable truss. Three conditions identify zero force members: (1) Two collinear members with non-collinear member and no external force, (2) Two non-collinear members with no external force, (3) Two intersecting members with equal and opposite forces. These rules simplify truss analysis by identifying removable members.

For indeterminate trusses: Strain Energy Method and Unit Load Method. Deflection formula: δ = Σ(PkL)/(AE), where P is force from actual loads, k is force from unit load. Zero force members are important for stability and should not be removed.

In truss analysis, a member is a zero-force member when three members form a joint with two collinear members and no external forces or support reactions applied at that joint, or when only two members form a joint with no external forces; these members carry no force and serve only as structural bracing.

To identify zero force members in a truss: (1) Start at joints with two collinear members and a third perpendicular member - the perpendicular member is a zero force member. (2) Move to adjacent joints and apply the same logic. (3) Continue systematically through the truss to identify all zero force members.

A truss is a pin-jointed structure where all joints are frictionless hinges, all members are straight, and all loads are applied only at joints, with self-weight neglected. For a truss to be stable and statically determinate, the number of members (m) must equal 2j - 3 for planar trusses or 3j - 6 for space trusses, where j is the number of joints. Forces acting toward a joint are compressive (negative), while forces acting away are tensile (positive). Zero force members can be identified when three members meet at a joint with two being collinear (the third is zero force), or when two non-collinear members meet at a joint with no external force (both are zero force members).

This video demonstrates how to design truss members for ultimate limit state by calculating axial forces (compression and tension) using trigonometry and verifying member capacity against buckling requirements, with key considerations including: (1) calculating support reactions for simply supported beams, (2) determining member angles using tan(θ) = depth/bay, (3) computing diagonal forces using sine and cosine relationships, (4) checking buckling capacity about the minor axis for unrestrained members, (5) installing intermediate restraints at 4.5m intervals for top chords to prevent major axis buckling, and (6) verifying tension capacity for bottom chords.

Support diagonals transfer vertical loads to supports, causing upper chord compression. Out-of-plane buckling occurs in half-sine wave form (μ=1.0), with calculated length equal to geometric length. In-plane buckling is shorter due to node restraints. For upper chords, out-of-plane calculated length equals geometric length, while in-plane length is shorter. For lower chords, both calculated lengths equal the distance between bracing nodes. When elements have different calculated lengths in plane and out-of-plane (e.g., L1 ≈ 2L), optimal sections require Iy ≈ 4Ix for equal slenderness ratios. Rectangular tubes with dimensions such as 126×9×3×0.343 mm (Iy/Ix ≈ 4) or 1238×343 mm (Iy/Ix ≈ 3.6) achieve equal stability in both directions.

This section covers truss member design for tension and compression. Truss members in tension are designed based on axial force and allowable stress. The required area is calculated as force divided by allowable stress. For members composed of multiple elements, the total area is divided among elements. The design considers slenderness ratio to prevent buckling. Truss members in compression are designed based on axial force, effective length, and allowable stress. The effective length is determined by distance between points of lateral restraint. The slenderness ratio is calculated as effective length divided by radius of gyration. The allowable stress is determined from slenderness ratio using buckling formulas. The required area is calculated as force divided by allowable stress. The design must consider local buckling of individual elements and overall stability. The effective length of truss members for buckling analysis depends on end conditions and points of lateral restraint. For members with pinned ends, effective length equals distance between supports. For members with fixed ends, effective length is half the distance between supports. The radius of gyration is determined from member section properties. The slenderness ratio is calculated as effective length divided by radius of gyration. The allowable stress is determined from slenderness ratio using appropriate buckling formulas.

A truss is a structural system composed of triangular elements that support loads. Real truss elements connect to plates through angles on both sides. The problem involves a planar truss with loads P and 2P at nodes B and C. The bars use two angles L12×66×6.4 with cross-sectional area 280 mm² and ultimate tensile stress of 390 MPa. Connections use 16mm diameter rivets to a 12mm thick plate. The rivets have ultimate shear stress of 190 MPa and bearing stress of 550 MPa. The goal is to find the allowable load P with a factor of safety of 2.5, considering tension in bars, shear in rivets, and bearing at connections.

Material efficiency measures total structural weight for given loads. V-shaped truss configurations follow cable behavior patterns, with columns propping apart top and bottom chords. Compression occurs along top chords while tension occurs along bottom chords. Bridge examples show tension members as slender rods while compression members are chunkier to resist buckling. K-trusses attempt improvements but often redistribute forces inefficiently. Optimized trusses maximize tension member lengths while minimizing compression member lengths, creating curved forms resembling arches with hanging cables. This optimization is specific to particular load conditions and locations.

This segment covers converting a frame model to a truss model and configuring 2D analysis. Frame elements can bend, but trusses only experience axial forces. Select all bars, then Assign > Frame > Partial Restrictions. For trusses in the XZ plane, restrict Moment 33 (bending moment) at both ends of each bar. Configure analysis options by restricting degrees of freedom to only X and Z directions (the truss plane), preventing Y-direction movement. This ensures the software correctly models the truss behavior without bending moments.

Static analysis differs fundamentally between 2D and 3D systems. In 2D, forces act along X and Y axes with moment equilibrium about the Z-axis. In 3D, forces act along all three axes with moments about each axis. Truss analysis assumes member weights distribute equally to connected nodes, forces act along member axes, and connections are frictionless pins. Structures are classified by static determinacy: isostatic structures have unknown reactions equal to equilibrium equations, while hiperstatic structures require additional compatibility equations. The method of joints solves truss forces by starting at joints with at most two unknowns and writing equilibrium equations (ΣFx = 0, ΣFy = 0). Space trusses extend 2D concepts to three dimensions, commonly used in large-span roofs, electrical towers, and stadium structures. Unlike 2D trusses where moment equilibrium about one axis suffices, 3D analysis requires force equilibrium in all three directions (ΣFx = 0, ΣFy = 0, ΣFz = 0) because moments can be generated about all axes.

This section covers truss and frame analysis methods. Zero-force members can be identified when: (1) A joint has only two non-collinear members with no external load, or (2) A joint has three members where two are collinear with no external load. For Y-shaped joints with no external load, all three members carry the same force type. The method of joints applies equilibrium equations at each joint, while the method of sections cuts through members to analyze one side. For frames with internal hinges, shear force at the hinge is found by taking moments about the hinge. For simply supported beams with uniform load w: maximum bending moment = (wL²)/8. The section modulus Z for rectangular sections is (bh²)/6. Maximum stress σ = M/Z = (3wL²)/(4bh²). For square sections, σ = (3wL²)/(4b⁴).

3D space frames are analyzed by decomposing them into 2D frames (XZ and YZ planes), with identical frames requiring single analysis. Loading differs between exterior and interior frames. Columns require force superposition with moments about global axes. Each member end has 3 displacements and 3 rotations, creating a 12x12 stiffness matrix. Torsion (GJ/L × θ) is an additional 3D effect. Bending requires different moments of inertia (Izz for vertical, Iyy for horizontal displacement). The local coordinate system requires X-axis along the centroidal axis, with Y and Z axes along principal section axes. Direction cosines extend 2D transformation to 3D by including all three axes.

This segment covers releasing moments and analyzing 3D trusses. 3D trusses require releasing moments at all joints to ensure they work as trusses (only axial forces). The software allows releasing moments in all directions (moments 2 and 3) at both ends of each member. After releasing moments, the analysis can be run and axial forces in each member can be displayed. The sign convention (positive for tension, negative for compression) must be understood.