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Created by rhiannonsian
almost 10 years ago
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Shear Force & Bending Moments
Beams Beams are structural members subject to lateral loads (forces/actions).They carry forces and transmit them to the supports. Finding the shear force and bending moment is an essential step in the design of any beam. The material of the beam suffers stresses when subjected to loads, and the member suffers deformation. Both stresses and deflections are directly related to the shear force and bending moments whose distributions along the length of the beam, including their maximum and minimum values, are important to calculate. It is important to understand not only the values, but the manner in which they vary along the member. Types of Beams There are three main types of beams: Simply supported beams - a beam with a pin support at one end and a roller support at the other Cantilever beam - fixed at one end and free at the other. At the fixed support the beam can neither translate nor rotate, whereas at the free end it may do both. Consequently both force and moment reactions may exist at the fixed end. Beam with overhang - a beam which is simply supported at two points but then extends past one of the supports. The overhang segment is similar to a cantilever except that the beam may rotate at point B.
Types of loads: Concentrated loads - eg p1, P2, P3, and P4 in the above figure Distributed load such as q in the above figure. Distributed loads are measured by their intensity which is expressed in units of force per uni distance (eg N/m). A UDL has constant intensity per specified distance. A varying load has an intensity that changes with the distance along the axis. Couple, illustrated by the couple of moment (M1) acting on the overhanging beam. Reactions If a beam is supported in a statically determinate manner, all reactions can be found from free body diagrams and equations of equilibrium.
Moment of a force Moment = Fa where F is the force acting and a is the perpendicular distance from the turning point (also known as the lever arm Moments haev a direction, and their value will be positive or negative depending on the direction in which they act Units are Nm, Nmm, kNm or kNmm A couple is defined as two equal parallel forces acting in opposite directions
Static Equilibrium When a system is in equilibrium: the algebraic sum of all horizontal forces is zero the algebraic sum of all vertical forces is zero the algebraic sum of the moments of all forces acting about a point is zero Equilibrium means that: There is no rotation There is no net force acting on the object
Shear force and bending moment diagrams (SFD and BMD) A shear force diagram is used to show the shear force along the length of a beam. A bending moment diagram shows how the applied loads on a beam create a moment variation along the length of a beam.These diagrams are used to determine the direct stresses through the beam due to bending moment and the shear stresses due to the shear forces.
Process for finding the shear force and bending moments Find the reactions at each support Imagine that the member is cut at that point; draw a free body diagram of either the LHS or RHS of the member. Replace the missing side of the member with force components in the x and y direction and a moment Apply the equilibrium equations Calculate the value of the two force components and the moment. These are called the normal force (N), shear force (V) and bending moment (M)
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