Question

The 40-ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the total required gap, 2*6, so that the rails just touch one another when the temperature is increased from T1 -20°F to T2 90 °F. If the rails were installed at -20 °F with this gap, what would be the axial force in the rails if the temperature were to rise to T3 = 110 °F. The cross sectional area of each rail is 6.10 in2. Est =29.000ksi 40 ft What is the total required gap to allow for thermal expansion (sum of gap at each end)? 0.10 0.35" 0.24" 0.43" What is the force in the rail due to the additional thermal expansion? -17.8 k -19.3 k -15.5 k -25.3 k

Answer 1

Solution. 1st paurt Gem donte auze Tニ-20F T 900F temgth of tne tack i 4oft the L= 404t OxI2 1mh So, we hmeu that thermal erpernsim Loefticient fan Now A A36 Steel s / 9- tue thermal expoms iom Here we will egnortion to fimd AL= L×ax ΔT .dro ant 2YStotne chmge m len gth AL = Case tenath AT chomge m temperatune = T2- T, pting the vodves we 0r12) AL= x6.6 X10 20) 96- -6 4807 6.61O AL= AL= 2S = 0.248 0 35 mch S0, the to te Tequined gar is o.251mch

2nd past No, tm th case, axial fonce it tre teper ature ices to 110 F. Sa fnd the we have to the fonce is change in length tre termpertune chanae equat to S0 basicnaln the dne to twit be 9f to 110 F cheange im leng th dve to the anin fosnee F. the below expsress t We S x AT Whre, 6 EE EX Floothicita F Fonce F Modnlu of A- Areo L- Jmitias Length S- chomge n F/A=S4 sess So, Com write n we S FL AE

So 1m tht cace A and E is 1Ne aven A- 6.10 im as 29000 Kse and L- imtial 1emath here And Puo deing tempenetre ane we aom 96f to 11b F. So, we have to at 90 F irmtiol Length Considen the Si upua -20 F at 90 F L Lengtn oat + chamge m length between -26 to 90 F = 40 + O.35 40.2S St 091 40.3512 1mch 5 L*dAT No, CTs-T) FL LX ax A E 40.35x12 66x1o- Cu6-96) Fx 40.35x1 2 29000x 6 10 Fe 23.35 ips 09A, Jreils dne to the fonce m the So2 23 35 kips thermal epansisn
Note: The above procedures are correct. So that the both part answers are correct. It is possible that the options may be incorrect. Kindly take that under consideration. Thank You.