Science Case

Aim : To determine the magnitude and the direction of the shear forces acting on beam.

Introduction : A material is said to be in shear if the force is applied to it tend to slide one face of the material over an adjacent face. Or it is defined as the strength of the component or material against the types of yield structural failures where the component and material fail in shear. For example the rivet holding the two flat piece of metal close together are in shear if the tensile force is applied to the plates, sufficient shear force could cause the rivet to fail. A simply supported beam subjected to vertical load is caused to a sag and as a result it subjected to shear force in two directions at right angle.

Application of shear force : used by the civil engineers when they project the beam into the roof .

Theory :

Beam : a beam that has hinged connection at one end and roller connection in other end is called simply supported beam

Cantilever beam : a beam which has two ends one end is rigidly built into the wall and the other end is free to move such a beam is called the cantilever beam.

Bending moment: suppose a cantilever beam is loaded by a tranverse point load W due this weight the beam is deflect downward .the bending effect at any section X is measured by the moment about the section of the load W. this moment is called the bending moment.

Shear force : the shear force at any section as the force transverse to the beam tending to cause it to shear across the section. Suppose there are a cantilever beam projected its one end into the wall and the one end is free to move, consider a load with magnitude W is placed at the free end for equilibrium the downward forces must be balanced by equal and opposite vertical reaction. Lets say it is AB. Consider now the effect of transverse saw cut at a section let say X of the beam . the effect of the load W would be to move the portion XB to downward .before saw cut there must have an upward force equal and opposite to W. opposing the tendency of the load to move the position XB downward. That force must be exerted by the material of the beam itself at the section X. the effect of the applied load at any section therefore it tends to shear the beam across at that section.

Shear force diagram: the shear force diagram is the graph plotted along the axis of the beam showing the variation of shear force along the beam the shear force is W is positive when it is uniform along the axis. Where the load is given dead load it may be given in unit of mass i.e.KG or TONNES and it is necessary to calculate the weight of such loads in force units ( newtons) before carrying our calculation.

Reaction force : it is a force which acting against the action force suppose we put the weight on the one end of the cantilever