A girder a span of 18mis simply supported at the ends. It is traversed by a train of loads as shown in fig. The 50 kN load loading. Find the maximum bending moment which can occur (i) under the 200 kN load (ii) Under 50 kN load, using influence line diagrams.

 A girder a span of 18mis simply supported at the ends. It is traversed by a train of loads as shown in fig. The 50 kN load loading. Find the maximum bending moment which can occur (i) under the 200 kN load (ii) Under 50 kN load, using influence line diagrams.

 

Solution:

 

a)               Maximum bending moment

 

i)                       Under   200   kN

loads.

To get the maximum bending moment under W3 the resultant R and W3 should be at equal distances from the center of the span C.For that the point of action of resultant R should be determined first.

 

a)  Resultant of loads:

 

R = 450 kN

 

Taking  moments      about

 

W4

 

200(3) +100 (3+2) +50(3 +2+3) = 450  x

 

-

x  = 3.33 from W4

b)  Bending moment under 200 kN load

 

Distance between C and 200 kN load = Distance between C and R = 0.33/2 = 0.165 m.

 

Ordiantes of ILD :

 

 

=2.05 m

 

Bending moment under the 200 kN load

 

=                                                               200 (4.5) + 100 (2.97) + 100 (3.52) +50 (2.05) = 1651.5 kNm.

 

(ii)               Bending moment under the load 50 kN load

 

To get the maximum bending moment under W1 , W2 and R must be at equal distances from the centre of span �. Distance between C and R = Distance between C and W1 = � (2 -0.33 + 3) = � (4.67) = 2.335 m

 

Ordinates of ILD:

 

 

Bending moment under the load 50 kN load

 

= 4.2 (50) + 3.09 (100) +2.35 (200) +1.24 (100) = 1113 kN m.