Module 3 · Lesson 3.2
Sign conventions, sagging and hogging
Getting signs right, and knowing which face of the beam is in tension.
Why this matters
Sign conventions cause more lost marks and more embarrassment than any other part of this subject. They are not deep — but they must be consistent, and you must be able to say what your sign means physically.
By the end of this lesson you should be able to
- State a sign convention and stick to it
- Read sagging and hogging from the sign of the moment
- Say which face of the member is in tension
This course uses one convention throughout. Shear force at a section is the sum of the upward forces on the piece to the left of the cut. Bending moment is positive when the beam sags — bending into a smiling curve, with the bottom face stretched.
Sagging means the top of the beam shortens and the bottom stretches, so the bottom is in tension. Hogging is the reverse: the top stretches and is in tension. This matters enormously in reinforced concrete, where the steel must go on the tension face — put it in the wrong face and the member cracks and fails.
Predict first
A cantilever sticks out from a wall and carries a load at its free end. Which face is in tension?
Practice
A cantilever 3.0 m long is fixed at the wall and carries a single point load of 12 kN at its free end. What is the magnitude of the bending moment at the wall?
Practice
A cantilever 2.5 m long carries a UDL of 8 kN/m over its whole length. What is the magnitude of the bending moment at the fixed support?
Practice
A simply supported beam of 6.0 m carries a central point load of 24 kN. What is the bending moment 2.0 m from the left support?
Summary
- State your convention, then never change it
- Sagging positive: bottom in tension; hogging: top in tension
- Being able to say which face is in tension matters more than the sign itself
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint