Bending Moment Abass Ajiboye & Mike Criollo Lalvay CEE 3710: Structural Modeling & Behavior

What is a bending moment? A Simple Illustration of Bending Moment Computing Bending Moment

Applying an upward force to ruler by pressing down the To calculate the bending moment about a reference point, 1 A bending moment is a reaction in an element measured in force × distance, and occurs as a result of external ends and having your thumbs push up against the ruler will we take the magnitude of the force and multiply it by the forces. cause the ruler to bend upwards. distance of the force from the point. Often this is calculated across the span of a member, which results in moment dia- 2 A bending moment will cause a bending effect on a gram. Note that the force must be perpendicular structural element. to the line between the point where the force is In the figure below, the force, F, causes a bending moment, applied and the reference point. For example: however we note that the beam does not break, this is because the bending moment due to F is being resisted by the Figure 2: beam. Suppose we double the force F and the beam snaps in half, in such a case the beam was unable to resist the The force applied by your fingers along with distance bending moment F caused. from a certain point along the ruler for which you were to measure the bend(which could be any point along the ruler) results in creating a bending moment in the ruler. Figure 4: Bending moment is proportional to compression and ten- sion in a flexural member which lead to the breaking and the bending moment at point A is simply the distance mul- buckling respectively of a flexural member. Hence, it is im- tiplied by the force. Therefore, the Bending Moment at portant to calculate the bending moment in members to Point A = 0.2(10) = 2 Nm. It is important to note prevent failure from stress due to bending. For example, that to use the above formula, the force (in this the ruler will snap under a very high bending moment. case a 10 N downward force) must NOT pass through the point. This is obvious, as if we ap- Figure 1: The vertical force, F, causes a bending moment which in turn cause the beam to bend. plied the same formula (distance * force) the distance would equal zero and therefore there Why it’s important would be no bending moment force

IMPORTANT TO NOTE. . . 1 Bending moment is important to civil and structural engineers because we can construct a bending moment That bending moment occurs only when a body(usually diagram for a building based on probable loads it may a deformable ﬂexural member or beam) is constrained experience. because an unconstrained body on the other hand will

2 A bending moment diagram tells us where an element not bend. Imagine placing the ruler on table with half of will experience the greatest bending moment, in other its length hanging out. Hitting the free hanging end of words it tells us where the element is most likely to break the ruler would result in the ruler ﬂipping over. This is due to bending. Figure 3: pure rotation and not bending.

3 We can then identify where an element is weakest and provide more reinforcement to resist bending.