Plots of internal V and M along a beam used to find critical sections.
Internal shear force V and bending moment M vary along a beam: dV/dx=-w and dM/dx=V. Plotted diagrams show where maxima occur. M is maximum where V crosses zero. Sign conventions must be consistent.
A simply supported beam with UDL w has Mmax=wL²/8 at midspan.
Shear and moment diagrams show where a beam is most highly loaded, so they guide where the section must be strongest.
Plots of internal V and M along a beam used to find critical sections.
Shear and moment diagrams show where a beam is most highly loaded, so they guide where the section must be strongest.
The slope of the shear diagram equals the negative of the load, and the slope of the moment diagram equals the shear force.
It usually occurs where the shear force passes through zero or at the point of the concentrated load.
Typical applications include finding the maximum bending moment in a simply supported beam, locating the critical section for a crane girder and planning the reinforcement of a floor beam under a point load.
Study "Power transmission shafts" first (topic 53 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Point load makes V jump. Moment jumps under applied couples. Area under V gives change in M.
A simply supported beam with UDL w has Mmax=wL²/8 at midspan.
The next topic is "Bending stress", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 54 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.