The cables of a suspension bridge have of 60m and a central dip of 7.5m. Each cable is stiffened by a girder hinged at the ends and also at the middle so as to retain a parabolic shape for the cables. The girder is subjected to a dead load of 10kN/m and a live load of 20kN/m, 15m long. Find the maximum tension in the cable when the loading edge of the live load is just at the centre of the girder. Draw also S.F. & B.M. diagrams for the girder.

Let us,

(1) Analyze the girder for live load:

Considering the girder as a simply supported girder and taking moments about the left end A,

$\sum M_A=0$

$-V_B\times 60+(20\times 15)\times(15+\frac{15}{2})=0$

$V_B=112.5kN$

$\sum F_y=0(\uparrow +ve)$

$V_A-(20\times 15)+112.5=0$

$V_A=187.5kN$

Beam moment at C

$BM@C=112.5\times 30=3375kNm$

Horizontal reaction for the cable

$H_e=\frac{B,M_C}{h}=\frac{3375}{7.5}=450kN$

Let …