Types Of Beams And Support Reactions

UNIT – I Basic Concepts of Engineering Mechanics Lecture 6: Types of members and supports and support reactions.

Beams 

A beam is generally considered to be any member subjected to principally to transverse gravity or vertical loading.

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The term transverse loading is taken to include end moments.

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There are many types of beams that are classified according to their size, manner in which they are supported, and their location in any given structural system.

Types of Beams 

Beams are generally classified according to their geometry and the manner in which they are supported

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Geometrical classification includes such features as the shape of the cross-section, whether the beam is – Straight or – Curved Or whether the beam is – Tapered, or – Has a constant cross section

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Beams can also be classified according to the manner in which they are supported.

Figure 6.1 Types of Beams Based on the Manner in Which They are Supported.

Fig 8.2 Simply Supported Beams in Buildings

Fig 8.3 Continuous Beams in Cable Stayed Bridge

Beams used in Buildings and Bridges – Girders Usually the most important beams, which are frequently at wide spacing. – Joist Usually less important beams, which are closely spaced, frequently with truss-type webs. – Stringers Longitudinal bridge beams spanning between floor beams. – Purlins Roof beams spanning between trusses. – Girts Horizontal wall beams serving principally to resist bending due to wind on the side of an industrial building. – Lintels Members supporting a wall over window or door openings.

Loading on Beams

Fig 8.4 Loading on beams, (a) axial (b) moment (c) concentrated and uniformly distributed with moment

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Beam can be subjected to concentrated loads or

distributed loads or combination of both.

Supports and Support Reactions: The three common types of connections which join a built structure to its foundation are- roller, pinned and fixed. A fourth type, not often found in building structures, is known as a simple support. This is often idealized as a frictionless surface). All of these supports can be located anywhere along a structural element. They are found at the ends, at midpoints, or at any other intermediate points. The type of support connection determines the type of load that the support can resist. The support type also has a great effect on the load bearing capacity of each element, and therefore the system.

If a support prevents translation or rotation of a body in a given direction, a force is developed on the body in that direction.

ROLLER SUPPORTS Roller supports are free to rotate and translate along the surface upon which the roller rests. The surface can be horizontal, vertical, or sloped at any angle. The resulting reaction force is always a single force that is perpendicular to, and away from, the surface. Roller supports are commonly located at one end of long bridges. This allows the bridge structure to expand and contract with temperature changes. The expansion forces could fracture the supports at the banks if the bridge structure was “locked” in place. Roller supports can also take the form of rubber bearing, rockers or a set of gears which are designed to allow a limited amount of lateral movements. PINNED SUPPORTS A pinned support can resist both vertical and horizontal forces but not a moment. They will allow the structural member to rotate, but not to translate in any direction. Many connections are assumed to be pinned connections even though they might resist a small amount of moment in reality. It is also true that a pinned connection could allow rotation in only one direction; providing resistance to rotation in any other direction. The representation of a pinned support includes both horizontal and vertical forces. FIXED SUPPORTS Fixed supports can resist vertical and horizontal forces as well as a moment. Since they restrain both rotation and translation, they are also known as rigid supports. This means that a structure only needs one fixed support in order to be stable. All three equations of equilibrium can be satisfied. The representation of fixed supports always includes two forces (horizontal and vertical) and a moment.

SIMPLE SUPPORTS Simple supports are idealized by some to be frictionless surface supports. This is correct in as much as the resulting reaction is always a single force that is perpendicular to, and away from, the surface. They are also similar to roller supports in this. They are dissimilar in that a simple support cannot resist lateral loads of any magnitude. The built reality often depends upon gravity and friction to develop a minimum amount of frictional resistance to moderate lateral loading.

Problem 6.1 Find the reaction at the supports of the following beam as shown in figure.

Problem 6.2 Determine the horizontal and vertical component of reactions at the fixed supports. Neglect the thickness of the beam.

Solution:

Problem 6.3 Determine the horizontal and vertical components of reactions of member AB, caused by a roller at A and a pin at B.

Solution:

Free Body Diagram