BEAM SYSTEM

BEAM SYSTEMS
1. CANTILEVER BEAMS  -  is a statically determinate structure .
2. Are built in at the supports . normally maximum moments shears are at ends . A
balcony of a building can be cantilevered to avoid supports columns at ends.
B
       A        
If  force W is placed at B of a cantilever L  then max moment is WL and max
shear is  W  at supports
 Doubling length will increase deflection by 8 x .  end B deflection is higher then
rest of beam .
The shape of the beam also decides on the deflection . Common timber beam is
rectangular .
The formula for bending stress in beams  f = My / I ( where I is the second moment of
area) gives an indication of the importance of  sections in beams.
A rectangular section having b & d as breadth and depth of section will have the
second moment of area to be bd3 / 12 . The higher I values will reduce the stress in the
beam section at the same moment force.  The value Y is the distance from centroid
and this shows that a taller section will give a higher  stress value .
Relation of cross sectional geometry to bending resistance ( same cross section area =
1cm2 ) ;
2x1/2   1x1  ½ x 2  1/4x4
1         2   4  8
W – point  Shear force can be vertical or horizontal
Shear resistance in beams  v = V. Q / I .b  ( Q is the first moment of area )
B.     Simply support beam systems
9 common in old buildings of timber and masonry where end joints are pinned .  
9 are normally determinate systems and can easily calculated
9 have maximum bending moments near center  and max shear near ends
9 self loads are treated as uniformly  distributed