--- title: "Internal hinge properties; point of contraflexure" subject: "Strength of Materials" chapter: 1 key: "semester_3/strength_of_materials:internal-hinge-contraflexure" source: https://www.bctengineer.com/q/semester_3/strength_of_materials/internal-hinge-contraflexure site: BCT Engineering --- # Internal hinge properties; point of contraflexure Strength of Materials · Chapter 1: Axial Forces, Shearing Forces and Bending Moments - Asked in: 2075 Chaitra, 2+2 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/internal-hinge-contraflexure - Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-1 ## Question Briefly explain the properties of internal hinge. What do you understand by point of contraflexure? ## Short answer An internal hinge transmits axial force and shear but no bending moment; it allows relative rotation, provides the condition ΣM=0, and reduces static indeterminacy by one. A point of contraflexure is where bending moment changes sign, reversing curvature. ## Answer #### Properties of an internal hinge An internal hinge is a pin connection inside a structure (for example in a beam or frame) that joins two parts. 1. It **transmits axial force and shear force** from one part to the other, but **cannot transmit bending moment**, so the **bending moment at the hinge is zero**. 2. It allows free relative rotation of the two connected parts, so the slope (rotation) is discontinuous at the hinge. 3. It provides **one extra equation of condition** ($\Sigma M_{hinge} = 0$ for the forces on either side). This is why a hinge reduces the degree of static indeterminacy by one (it releases one internal moment) and can make a structure with extra reactions determinate (for example, a three-hinged frame). 4. Hinges must be located and counted carefully: too many hinges turn the structure into a mechanism (unstable). 5. A hinge is a point of zero bending moment, but not necessarily a point of contraflexure, because the moment need not change sign there. #### Point of contraflexure A point of contraflexure is a point on the span of a beam where the bending moment changes sign (from sagging to hogging or the reverse), passing through zero. The curvature of the elastic curve changes direction there. It is found by setting $M(x) = 0$. Such points matter in design: the moments on either side have opposite signs, so the tension face switches from the bottom to the top, and reinforcement can be curtailed or shifted there. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does an internal hinge transmit between two parts? A. Axial and shear force but no bending moment B. Bending moment only C. Nothing D. Bending moment and shear but no axial force Answer: A. A pin allows free rotation, so the bending moment there is zero, while axial and shear forces are carried across. (Key point: What a hinge transmits) 2. How does an internal hinge help in analysis? A. It adds a fourth equilibrium equation for the loads B. It makes the structure unstable always C. It provides one extra equation (M_hinge = 0), reducing the degree of indeterminacy by one D. It removes shear force Answer: C. The condition sum M_hinge = 0 for the forces on one side gives an extra equation, so a structure with an extra reaction can become determinate. (Key point: Extra equation of condition) 3. Which statement about a hinge and a point of contraflexure is correct? A. Every hinge is a point of contraflexure B. A hinge has zero moment, but it is not necessarily a point of contraflexure because the moment need not change sign C. A point of contraflexure has maximum moment D. They are always at the same place Answer: B. Contraflexure needs the moment to pass through zero and change sign, which does not happen at every hinge. (Key point: Point of contraflexure) ## Related in Strength of Materials - [Point of contraflexure; w-V-M relation](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Acontraflexure-load-shear-moment-relation) — Strength of Materials, chapter 1 - [Frame AFD, SFD, BMD (5 kN/m, 10 kN, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-5knm-10kn) — Strength of Materials, chapter 1, asked 2× - [Frame AFD, SFD, BMD (5 and 10 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-5knm-10knm) — Strength of Materials, chapter 1, asked 2× - [Frame SFD, BMD (100 kN, 20 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-sfd-bmd-100kn-hinge-60deg) — Strength of Materials, chapter 1 - [Frame AFD, SFD, BMD (12 kN, 25 kNm, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-afd-sfd-bmd-12kn-25knm) — Strength of Materials, chapter 1 - [Beam AFD, SFD, BMD with hinge (80 kN)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Abeam-afd-sfd-bmd-20knm-80kn) — Strength of Materials, chapter 1 ## Related in other subjects - [AFD, SFD, BMD for frame with internal hinge](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-internal-hinge-5kn-per-m) — Applied Mechanics, chapter 6 - [Shape factor, plastic hinge properties, T-beam](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Ashape-factor-t-beam-plastic-hinge) — Theory of Structures II, chapter 5 - [Bezier properties; point at u=0.2](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Abezier-properties-point-u-0-2) — Computer Graphics, chapter 5, asked 2× - [AFD, SFD, BMD of frame with hinge at D](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-bmd-8knm-hinge-50kn) — Applied Mechanics, chapter 6