Question

Three boards, each 50 mm thick, are nailed together to form a beam that is subjected to a 1200-N vertical shear. Knowing that the allowable shearing force in each nail is 600 N, determine the largest permissible spacing s between the nails. 50 mm 100 mm 50 mm 50 mm 150 mm The largest permissible spacing between the nails is mm.

Answer 1

Solution :- First Let us find the moment of inertia of the given I- section. Cabout cenbroid) I= I1+I2+I3 50 mm O since I1 = I3 Id=75mm I =2Ij + I2 loomm 50 mni bly3 12 II 50 mm + Aid ² 150 mm 150X503 +1150X50 ) X752 12 = 43.75 X106 mm 4 Iz b2 h₂3 50 X 1003 11 - : 4.167 X106 mm 4. 12 12 .: I = 2 x 43.75X106716167x 106 I = 91.667X106 mmt Since the vertical shear force ou beam V = 1200 N Allowable shear force in each nails F =600N.

the nails , Ś= 81.482 mm Force in the nails can be given as follows va F = I 5-0 S = specing as mentioned in question) Q can be calculated as follows 150 mm Q ИА somm - 75 (150 X 50) 75mm 5625.00 mm3 Q Now putting all the valles in eq o we get, s 600 = 1200 X 562500 91.667 X 106 600 x 91.667X106 S = 1200 X 562500 S = 81.482 mm Answer:- The largest permissible spaling between