three moment theorem sam zou 3/6/2018 · three moment theorem sam zou 3/6/2018 span a = 24ft span b...
TRANSCRIPT
Three Moment TheoremSam Zou3/6/2018
SPAN A = 24ftSPAN B = 9ftSpan C =10ftUniform load on span A, w1=3klfUniform load on span C, w2=6klfPoint load on span b, P=104kDistance to point load P from R2, D=6ft
1. Use three Moment Theorem to solve internal moments
2. Solve Support reaction R1, R2, R3
Make free body diagram of span A and B.
- Make free body diagram of span A
- Make free body diagram of span B
- Make free body diagram of span C
- Double Check
ΣM@R2 =R1 (A)-W1(A/2)+|M2|=0
ΣFv =R1 -W1+V1=0
ΣFv =R2 -P+V2=0
ΣF =R1+R2+R3-W1-P-W2=0
ΣM@R3 =R2 (9)-P(3)-1.7(9)-|M2|+|M3|=0
ΣM@R3 =R4 (C)-W2(C/2)-|M3|=0
ΣM@R4 =R3 (C)-W2(C/2)+|M3|-V2(C)=0 =R3 (10)-60(5)+77.9-14.16(10)=0 R3 =95.3
=R4 (10)-60X(5)-77.9=0 R4 =22.2k
=R2 (9)-104(3)-1.7(9)-184.2+77.9=0
=R1 (24)-24x3x(24/2)+184.28=0R1 = 28.3 k
R2 = 90.16k
V1=1.7k
V2=14.16k
=M1=0
=WL2/24=17282M2(24+9)+M3(9)=6(1728+416)
M2(9)+2M3(9+10)=6(520+250)
=4PL2/81 =416
Make free body diagram of span B and C.
=M2 =M3
M2=-184.28 k-ft
M3=-77.9 k-ft
L1 = A L2 = B
=M2
=5PL2/81=520 =WL2/24 =250
=M3 =M4 =0 L1 = B L2 = C
R1
R2
R3 R4
V1
V2V1
V2
M2
M2
M3
M3