Internal forces in arches – direction of the shear force component In a solid arch under general loading, the internal shear force at a section acts:

Introduction / Context:
Arches carry load through a combination of normal thrust (along the arch axis) and shear (radial) components. Correctly identifying the direction of these internal forces is essential for section design and for interpreting influence lines in arch analysis.

Given Data / Assumptions:

• Solid arch of arbitrary profile in a vertical plane.
• Section taken at an arbitrary point on the arch axis.
• Internal force components resolved relative to the local axis of the arch.

Concept / Approach:
At any section of an arch, the internal forces are typically expressed as: (i) normal thrust along the tangent to the axis, (ii) radial (or shear) force perpendicular to the axis, and (iii) bending moment about the out-of-plane axis. The “shear force” in arch theory is the radial component normal to the axis.

Step-by-Step Solution:
Resolve internal action at a section into two in-plane components: N_t (tangential, along the arch) and V_r (radial, perpendicular to the arch).By definition, V_r is the shear force in arch analysis, so it acts normal to the axis.Therefore, the correct directional description is “perpendicular to the axis of the arch”.

Verification / Alternative check:
Textbook free-body diagrams of arch segments consistently show normal thrust and radial shear at the cut, plus a bending moment.

Why Other Options Are Wrong:

• (a) fixes the shear direction as vertical, which is not generally true for curved axes.
• (b) is the direction of normal thrust, not shear.
• (d) again corresponds to the tangential component (normal thrust), not shear.
• (e) is unnecessary because (c) is correct.

Common Pitfalls:
Confusing “shear” in beams (vertical) with “radial shear” in arches; always resolve relative to the local arch axis.

Final Answer:
Perpendicular to the axis of the arch (radial direction)