what is the moment amplification factor, B1, for the member shown in Problem 6.2-2?a. Use LRFDb. Use ASD 2 How much service live load, in kips per foot, can be supported? The memberweight is the only dead load. The axial compressive load consists of a ser-vice dead load of 10 kips and a service live load of 20 kips. Do not considermoment amplification. Bending is about the x axis, and the steel is A992.a. Use LRFD.b. Use ASD.20'–W18 X 86FIGURE P6.2-2

Euler’s Buckling Load can be calculated as; Pel= π2EI*(K1L)2 Where, EI*- is the reduced stiffness of the member . K1L- the effective length of member L - is the length of the member In the direct analysis method, EI* = 0.8τbEIx Substitute the values in above expression; Pel= π2EI*(K1L)2Pel= π20.8τbEIx(KxL)2 where, E - the elastic modulus of steel Ix - is the moment of inertia of section about major principal axis Kx - is the buckling factor about x-axis . L - is the length of member . Substitute 29000 ksi for E, 1750 in4 for Ix, 1.0 for τb, 1.0 for Kx, 20 ft × 12 in.1 ft for L. Pel= π2 × 0.8 × 2900 × 1750(1.0 × 20 × 12)2= 6956.7 kips Computing the moment factor Cm as follows: For a transversely loaded member, the value of Cmis taken to be 1.0. Member is transversely loaded Cm = 1.0 The moment amplification factor B1 is calculated as. (a) LRFD method: B1 =Cm1-αPuPel Where, the value of the constant α is 1.0 and Pr is the axial load on the member. Pr = Pu where, Pu is the factored load on member. factored load on the member is calculated as: Pu =1.2PD + 1.6PL where, PD is the axial dead load , PL is the axial live load. Substituting values in above expression Pu =1.2PD + 1.6PL= (1.2 × 10 + 1.6 × 20)=44.0 kips Moment amplification is calculated as; B1 =Cm1-αPuPel Substitute value in above expression B1 = 1.01-1.0×446956.7= 1.01 Therefore, the moment amplification factor is 1.01 (b) ASD method: B1 =Cm1-αPaPel Where, the value of the constant α is 1.6 and Pa is the allowable load on the member. Allowable load on the member is calculated by: Pa = PD+PL Substitute the values in above expression where 10 kips for PD and 20 kips for PL. Pa = PD+PL= 10+20=30 kips Moment amplification can be calculated as: B1 =Cm1-αPuPel Substitute the values in above expression where 1.0 for Cm, 30 kips for Pa, 1.60 for and 6956.7 kips for Pel. B1 =1.01-1.60×306956.7=1.01 Therefore, the moment amplification factor is1.01.