# Bending Moment and Shearing Force

Basic structural learning begins with an analyzing of a simply supported beam. A beam is a structural member (horizontal) that is design to support the applied load (vertical). It resists the applied loading by a combination of internal transverse shear force and bending moment. An accurate analysis required in order to make sure the beam is construct without any excessive loads which affect its strength.

A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m). The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.

A shear stress, denoted [pic](Greek: tau), is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section. Normal stress, on the other hand, arises from the force vector component perpendicular or antiparallel to the material cross section on which it acts.

Objective : To show that at any section of a beam subjected to transverse loads;

i. The shearing force is defined as the algebraic sum of the transverse components of the forces to one side of the section.

ii. The bending moment is defined as the algebraic sum of the moments of the forces to one side of the section.

The applications of the experiment are to study about how to establish the shear and moment for beam and shaft. Beam and shaft are important structural and mechanical element in engineering.

THEORY

Consider the cantilever beam shown subjected to a number of transverse loads

[pic]

At any transverse section X-X:

1. the shearing force:

Q=W3-W2-W1

Q=∑W

2. the bending moment:

M=W3x3-W2x2-W1x1

M = ∑ WX

Apparatus

[pic]

Note-Sign convention

Upward forces to the left of any section are considered as positice forces and downward forces as negative forces producing positive or negative values of Q and M as shown below. [pic]

Procedure:

i. The beam (1) was checked to be in the equilibrium position, without a load applied. The support tension springs were adjusted to allow the beam (1) to be in equilibrium position.

ii. The load hanger (2) and weight(s) were attached to the beam (1) at position x1, and weights were added to hangers (3) and (4) until the beam reaches equilibrium position.

iii. The experiment was repeated with load hanger (2) and weights in position x2 and x3.

iv. The values for every position of the load (W) are recorded.

v. A shearing force diagram and bending moment diagram is drawn.

RESULT

Load: 50 gram

|Distance (m) |Experimental Value |Theoretical Value | | |W1(N) |W2(N) |W2 x a (Nm) |Qx(N) |Mx(Nm) | |x1 |0.588 |0.6867 |0.06867 |0.4905 |0.07357 | |x2 |0.588 |0.4905 |0.04905 |0.4905 |0.04905 | |x3 |0.588 |0.1962 |0.01962 |0.4905 |0.02452 |

Load: 100 gram

|Distance (m) |Experimental Value |Theoretical Value | | |W1(N) |W2(N) |W2 x a (Nm) |Qx(N) |Mx(Nm) | |x1 |0.4905 |1.4715 |0.14175 |0.981 |0.14715 | |x2 |0.4905 |0.981 |0.0981 |0.981...

References: 5. R. C. Hibbeler, Mechanics of Statics, 2005, Prentice Hall

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