Different Types of Beams | What is Beam? |

4.2 BEAMS

* A beam is a structural element which has one dimension (length) considerably larger than the other

two dimensions in the cross section and is supported at a few points.

* Types of supports: Simple supports, roller supports—hinged support and fixed support

Types of Beams:

1. Determinate Beams: cantilever, simply supported, one end hinged and other on roller,

overhanging

2. Indeterminate Beams: both ends hinged, propped cantilever, continuous.

Statically determinate beams are the beams, in which all reaction components at supports can be

found using the equations of equilibrium only.

* Types of Loadings: Concentrated load, uniformly distributed load (UDL), uniformly varying load

(UVL) general loading, external moments.

Analysis of Pin-Jointed Plane Frames

* A pin-jointed frame is a structure made of slender members pin connected at ends and capable of

taking loads at joints.

* A perfect frame is the one which retains its shape with minimum number of members and can carry

loads applied at joints.

* A frame is said to be deficient, if the number of members in it are less than that required for a

perfect frame.

* A frame is said to be redundant, if the number of members in it are more than that required for a

perfect frame.

* The assumptions made in the analysis of pin-jointed frames are:

1. The ends of members are pin-connected.

2. The loads act at joints only.

3. Self weight is negligible.

4. If there are a number of members along a line of truss, they are located along the same

longitudinal line.

FRICTION

* Friction is the resistance to motion offered by minutely projecting particles at the contact surfaces.

* The limiting value of frictional force when the motion is impending, is known as limiting friction

upto this state it is static friction.

* The friction experienced by a body while in motion is known as dynamic friction. It may be sliding

friction or rolling friction.

* The ratio of limiting friction to normal reaction is known as coefficient of friction.

* Coulomb’s laws of friction:

1. Friction always opposes motion

2. Till the limiting value is reached, the magnitude of friction is exactly equal to the force which

tends to move the body.

3. Coefficient of friction for two contacting surface is constant.

4. Frictional force depends upon the roughness of the surfaces in contact.

5. Force of friction does not depend upon the area of contact.

6. Coefficient of dynamic friction is less than coefficient of static friction.

* The angle of limiting friction is the angle between the resultant reaction and the normal to the

horizontal plane on which the motion of the body is impending.

* The maximum inclination of the plane on which a body, free from external forces, can repose

(sleep) is called angle of repose.

* The inverted cone with semi-central angle a equal to limiting angle of friction is called as cone of

friction.

* Rope/belt friction:

T2 = T1 emq

where T1 = force on slack side

T2 = force on tight side

m = coefficient of friction

q = angle of contact.