# Shear Force

Topics: Force, Shear stress, Shear strength Pages: 7 (1838 words) Published: October 31, 2012
CEMB 121 MECHANICS OF MATERIALS LABORATORY
EXPERIMENT (NO.2 (a))
SHEAR FORCE I

SUMMARY
Shear Forces occurs when two parallel forces act out of alignment with each other. For example, in a large boiler made from the sections of sheet metal plate riveted together, there is an equal and opposite force exerted on the rivets, owing to the expansion and contraction of the plates. The shearing force (SF) at any section of a beam represents the tendency for the portion of the beam on one side of the section to slide or shear laterally relative to the other portion.

The diagram above shows a beam carrying loads W1, W2 and W3. It is simply supported at two points where the reactions are R1 and R2. Assume that the beam is divided into two parts bya section X-X. The resultant of the loads and reaction acting on the left of A-A is vertically upwards and since the whole beam is in equilibrium, the resultant force to the right of A-A must be F downwards. F is called the Shearing Force at the section A-A. It may be defined as follows; the shearing force at any section of a beam is the algebraic sum of the lateral components of the forces acting on either side of the section. Where forces are neither in the lateral or axial direction, they must be resolved in the usual way and only the lateral components are used to calculate the shear forces. There is different types of load. A beam is normally horizontal and the loads vertical. Other cases which occur are considered to be exceptions. A concentrated load is one which can be considered to act at a point, although in practice it must be distributed over a small area. A distributed load is one which is spread in some manner over the length or a significant length of the beam. It is usually quoated at a weight per unit length of beam. It may either be uniform or vary from point to point.

STATEMENT:
This test is performed to determine that the shear force at a cut section of a beam is equal to the algebraic sum of the forces that acting to the left or right of the section. The shear strength is one of the most important engineering properties in this experiment. The shear strength is needed for engineering situations such as determining the stability of slopes of cuts and calculating the pressure exerted by a load on a beam.

INTRODUCTION:
Moving loaads on beams are common features of design. Many road bridges are constructed from beam, and such have to be designed to carry a knife edge load or a string of wheel loads or a uniformly distributed load or perhaps the worst combination of all three.

OBJECTIVE:
To show that the shear force at a cut section of a beam is equal to the algebraic sum of the forces that acting to the left or right of the section. THEORY:

Shear force at section x-x is;
S.F x-x= W1+ W2+ W3- RA
Or,
S.F x-x= RB

APPARATUS:
1. A pair of simple supports
2. Special beam with a cut section
3. A set of weights with several load hangers

PROCEDURE:
1. The load cell was connected to the digital indicator.
2. The indicators were switched on. Before take the readings, the indicator must be switched on 10 minutes for stability of the reading the indicator. 3. The two simple supports were fixed to the aluminum base at a distance equal to the span of the beam to be tested. The supports were screwed tightly to the base. 4. The load hanger was hanged to the beam.

5. The beam was placed on the supports.
6. The load hangers were placed at the desired location.
7. The indicator reading was noted. The tare button on the indicator was pressed if it is not zero. 8. A load was placed on each load hanger.
9. The indicator reading was recorded. These represent the shear force at the cut section. 10. All loads were removed from the load hangers and a different set of loads were applied and at different locations. 11. Step 6 to 11 was repeated for another 5 sets of readings.

RESULTS
Beam span = 800...