Parabolic versus circular arch
Solve reactions, horizontal thrust, section resultants, shape effects, and imposed-movement compatibility for determinate arches.
Open the complete lessonAdvanced engineering statics simulation
Three-Hinged Arch Engineering Suite
Reactions, crown thrust, section resultants, shape effects, and imposed-movement compatibility.
Compare the funicular parabolic profile with a valid minor circular arc under the same vertical UDL.
Model scope and verification
Scope: Planar, equal-elevation, pin-connected three-hinged arch unless the imposed-movement scenario is selected. Normal force is positive in compression. A section coincident with the point load uses the explicitly selected left or right face. Circular comparison is restricted to a single-valued minor arc with h ≤ L/2. The UDL acts vertically and is uniform per horizontal metre.
Acceptance check: Solve the equivalent simply supported beam reactions, enforce zero crown moment for H, use M_arch = M_beam − Hy, draw the cut normal to the arch tangent, and reconstruct global section-force components from N and V.