A 3 hinged arch of span 40m and rise 8m carries concentrated loads of 200 kN and 150 kN at a distance of 8m and 16m from the left end and an udl of 50 kN/m on the right half of the span. Find the horizontal thrust.

 A 3 hinged arch of span 40m and rise 8m carries concentrated loads of 200 kN and 150 kN at a distance of 8m and 16m from the left end and an udl of 50 kN/m on the right half of the span. Find the horizontal thrust.

Solution:

(a) Vertical reactions VA and VB :

 

Taking moments about A,

200(8) + 150(16) + 50 * 20 * (20 + 20/2) -VB (40) = 0

1600 + 2400 + 30000 -40 VB = 0

VB= = 850 kN

VA = Total load -VB = 200 + 150 + 50 * 20 -850 = 500 kN

 

(b) Horizontal thrust (H)

 

Taking moments about C,

-H x 8 + VA (20) -200 (20 -8) -150 (20 -16) = 0 -8H + 500 * 20 -200 (12) -150 (4) = 0

 

H = 875 kN