Please make sure you use the right dimensions and make sure you use the right fo
ID: 1713476 • Letter: P
Question
Please make sure you use the right dimensions and make sure you use the right formulas!! Check you work! Thanks!
3. For the floor plan shown below, design members B1 and G1 for bending, shear and deflection. Compare deflections with L/240 for total loads and L/360 for live loads. The steel is ASTM A992., Grade 50; you may assume that Cb-1.0 for bending. The dead load (including the beam weight) is assumed to be 85 psf and the live load is 150 psf. Assume that the floor deck proveds full lateral stability to the top flange of B1. Ignore live load reduction. Use the design tables in the AISCM where appropriate. Remember to check any assumptions you make. 1 6'-8 G1 6'-8" 6'-8 30'-0" 30-0"Explanation / Answer
Design of B1:
Tributary width =6'8"=6.67 feet
Dead load on beam = 85*6.67=566.67 plf=0.5667 kip/ft
live load on beam = 150*6.67=1000 plf=1 kip/ft
design moment on beam = (1.2*0.5667*302/8)+(1.6*1*302/8)=256.5 kip-ft
Design shear force on beam = (1.2*0.5667*30/2)+(1.6*1*30/2) = 34.2 kips
Use W16x40
Moment capapcity of beam = 274 kip-ft
Shear capapcity of beam = 146 kips
Moment of inertia of beam = 518 in4
Deflection of beam due to total load = [(5*(0.5667+1)/12)*(30*12)4]/(384*29000*518) = 1.9 in
L/240 = 30*12/240=1.5 in
Let us provide a stiffer beam
Let us consider W21x44
Moment of inertia=843 in4
Total deflection of beam = [(5*(0.5667+1)/12)*(30*12)4]/(384*29000*843)=1.17 in(<1.5 in)
deflection of beam due to live load = [(5*1/12)*(30*12)4]/(384*29000*843)=0.745 in
L/360 = 360/360=1 in
Therefore the deflection is also within limit
provide W21x44 as B1
Design of G1 :
The girder is subjected to concentrated force coming from 4-B1 beams supported on it
Factored concentrated force coming on girder from each B1 =34.2 kips
Maximum shear force in girder = 4*34.2/2=68.4 kips
Maximum moment in girder = 68.4*6.67=456 kip-ft
Let us consider W24x55
Moment capacity of beam for unbraced length of 6.67 ft = 460 kip-ft
Shear force capacity of beam = 252 kips
Deflection check:
service level dead load on girder from each beam B1 = 0.5667*15=8.5 kips
service level live load on girder from each beam B1=1*15=15 kips
Moment of inertia of W24x55 = 1350 in4
Deflection of beam due to total load = (23/648)*(30+17)*(20*12)3/(29000*1350)=0.589 in
L/240 = 20*12/240=1 in
deflection of girder due to live load = (23/648)*(30)*(20*12)3/(29000*1350)=0.376 in
L/360 = (20*12)/360=0.67 in
Let us provide W24x55 as girder