I'm heading home from Manmad. It's 1 AM, the train is almost two hours late. After waiting for a bit at the station, the train finally arrives. I pick up the bags and board the train. S-6 looks more like a 'General' coach, with people sleeping in the aisles. I finally get to my berth - it's a middle berth. The berth is set into place, and I'm about to lie down. I suddenly notice that one of the chains holding up the berth is not taut. The entire berth is being supported by only one chain.
It makes me a little uneasy, but since there's nothing I can do, I try to sleep. The uneasiness just won't go. I keep wondering, will a single chain safely hold up my weight? The uneasiness gives way to calculation...
Approximate oval chain links as rectangular chain links (Since I've never been able to calculate stresses in curved members with a calculator, and certainly wasn't going to succeed with mental math)
Therefore, the links can fail in shear.
Yeild Strength of Mild Steel - Approximately 200 MPa (Close enough)
Shear strength is taken to be half of the Tensile Strength - 100 MPa
Diameter of chain links - 5 mm (Measured by 'looking')
Cross sectional area - (Pi/4)*5*5 = approx 20 sq. mm (actually 19.63)
Load on chain links - 90Kg x 9.8 = approx 900N(My weight + weight of berth)
Shear stress on any chain link - 900/20 = 45MPa
Permissible Shear Stress - 100 MPa
Conclusion : The berth will not fall, even though only one chain is holding it up.
Reassured, I sleep.