For the three-hinged arch shown determine the reactions at hinges A and C in new

Question

For the three-hinged arch shown determine the reactions at hinges A and C in newtons. (Assume that the +x-axis is to the right and the ty-axis is up along the page. Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 400 N 895 N 45° 6.93 6.93 magnitude direction Select- magnitude directiorn -Select-- magnitude direction Cy magnitude direction -Select-- Select- Determine the horizontal and vertical components of force that pin B exerts on each member in newtons. (Enter the magnitude.)

Explanation / Answer

The problem can be solved using equilibrium equations

Considering moment equilibrium about support C,we get

Ay(6.93+6.93+4+4)=400*(6.93+4+4)+895*4

Ay = 436.96 N(vertically upwards)

from equilibrium of forces in vertical direction,

Cy = 400+895-436.96=858.04 N (vertically upwards)

Since there is internal hinge at B,bending moment at B=0

Therefore, (436.96*2*6.93)-400*6.93-Ax (13.86tan30)=0

Ax = 410.43 N (towards right)

Cx=-Ax=-410.43 N = 410.43 N(towards left)

Force exerted by Pin B on members are:

Bx=410.43 N

By = 436.96-400=36.96 N

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