__Answer:__ yes

**Question:** In the following diagram; determine

**force** and

**nature** of force in

**member AB** (HINT: determine reactions first)

I managed to get AB as 16.28822036 kN tension.

A brief description of how I did it.

I got the angle under the bridge 12.52880771 (the line from RB to B and the angle between that to horizontal). Using this angle, I then got the vertical distance from the horizontal to B by using trig with the 3m that is given. This distance was 2/3 m.

Now having this distance, I could get the hypotenuse which is RB to B and also the distance of the vertical bar from B. RB to B is square root of (85/9). The distance of the vertical bar from B is 2 and 1/3 m. (3m subtract 2/3 m).

Now cutting it and looking at the RHS, I summed it at B (canceling AB and the hypotenuse I was talking about), and got the top bar's force. I got this as 87 1/7 kN in tension. (This will be useful later on)

Now I look at the LHS. Using the hypotenuse distance square root of (87/9) and also the 3m given I get the area of the triangle RB - A - B. I do this by using 1/2*a*b*sinC. C is worked out by 90 degrees minus the angle under the bridge. (90 - 12.52880771 = 77.47119229). (I get area as 4.5m^2)

Now this area has to equal the other area equation, 1/2*base*height. The height is always perpendicular, so this is what I want, as it is the perpendicular distance from AB to RB. So I need to base, I calculate the base by using a^2 = b^2 + c^2 - 2bc*cos angle. The a is the base, and the rest are form the triangle. I calculate the base as 3.80058475m. Thus height is 2.368056652m. (This is the perpendicular distance between the line AB and the point RB).

Now I sum it at RB, since I sum at RB, the horizontal component of RA is canceled and the force on RB-B is also canceled. This leaves the vertical component of RA (100 kn), AB and the top bar (87 and 1/7 kn in tension).

Thus, 0 = (-100) * 3 + (87 1/7) * 3 + AB * 2.368056652.

AB = 16.28822036kN tension.

I have no idea if this is right. This process is so convoluted that there is a high chance of error throughout the process. What do you guys think?

There must be a better and simpler way than this.