a b c
d
L1 L2
L3
P
R1
R2
CVEN 345 Quiz B Problem 1
Mo
-P*L1
L1 L2
L3
m1
m2
1
1
L1 L2L3
L1 L2L3
1*L3
1*L31*L3
1*(L1+L2)1*L2
Required moment diagram shapesValues vary by student exam
m1
m2
1
1
L1 L2L3
L1 L2L3
1*L31*L31*L3
1*(L1+L2)
Mo- P*L1
L1 L2
L3
1*L2
P
CVEN 345 Quiz B Problem 1
m1
m2
1
1
L1 L2L3
L1 L2L3
m2=1*L3
m1=1*L3m1=1*L3
m3=1*(L1+L2)
M0
M1 = - P*L1
L1 L2
L3
m4=1*L2
P
DeltaBig10 = Integral(M0*m1*dx)/EIVolume Int = (1/2)(M1*m1)(L1)/EI = - (1/2)(P*L1)(1*L3)(L1)/2)/EI
DeltaBig20 = Integral(M0*m2*dx)/EIVolume Int = (1/6)(2m3+ m4)*M1*L1/EI
For L1=8, L2=12, L3=10, P=10:DeltaBig10 = (1/2)(20*8*10)(8) = -6400/EIDeltaBig20 = (1/6)(2*(8+1
m1
m2
1
1
L1 L2L3
L1 L2L3
m2=1*L3
m1=1*L3m1=1*L3
m3=1*(L1+L2)
M0
M1 = - P*L1
L1 L2
L3
m4=1*L2
P
DeltaLittle11 = Integral(m1*m1*dx)/EI Volume Integral (m1*m1)(L1+L2)/EI + (1/3)(m2*m2)*(L3)/EI
DeltaLittle12 = Integral(m1*m2*dx)/EI = (1/2)(m1*m3)(L1+L2)/EI + + 0
DeltaLittle22 = Integral(m2*m2*dx)/EI = (1/3)(m3*m3)(L1+L2)/EI + 0
D1 = D10 + d11 R1 + d12 R2 + d13 R3 + d14 R4 + d15 R5 + d16 R6 + d17 R7 + d18 R8 + d19 R9
D2 = D20 + d21 R1 + d22 R2 + d23 R3 + d24 R4 + d25 R5 + d26 R6 + d27 R7 + d28 R8 + d29 R9
D3 = D30 + d31 R1 + d32 R2 + d33 R3 + d34 R4 + d35 R5 + d36 R6 + d37 R7 + d38 R8 + d39 R9
D4 = D40 + d41 R1 + d42 R2 + d43 R3 + d44 R4 + d45 R5 + d46 R6 + d47 R7 + d48 R8 + d49 R9
D5 = D50 + d51 R1 + d52 R2 + d53 R3 + d54 R4 + d55 R5 + d56 R6 + d57 R7 + d58 R8 + d59 R9
D6 = D60 + d61 R1 + d62 R6 + d63 R3 + d64 R4 + d65 R5 + d66 R6 + d67 R7 + d68 R8 + d69 R9
D7 = D70 + d71 R1 + d72 R2 + d73 R3 + d74 R4 + d75 R5 + d76 R6 + d77 R7 + d78 R8 + d79 R9
D8 = D80 + d81 R1 + d82 R2 + d83 R3 + d84 R4 + d85 R5 + d86 R6 + d87 R7 + d88 R8 + d89 R9
D9 = D90 + d91 R1 + d92 R2 + d93 R3 + d94 R4 + d95 R5 + d96 R6 + d97 R7 + d98 R8 + d99 R9
12
CA B D E F H
8 8 12 12 12 10 10
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVB1.0
1.0
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVB1.0
L2L1 L1 L2 L2 L2 L3 L3
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVG
128 8 12 12 12 10 10
1/48 = left end/64 so LE moved up 1.333
0.333
1/48 = right end/20 so K moved down 0.417
-0.417
1.0
-1.0
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVG
L2L1 L1 L2 L2 L2 L3 L3
y1
y2
1.0
-1.0
y1 = L1/2L2 y2 = L3/2L2
L2L1 L1 L2 L2 L2 L3 L3L2L1 L1 L2 L2 L2 L3 L3
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILMD
128 8 12 12 12 10 10
36/48 as LeftEnd/16 so left end moved down 12
36/48 as right end up/68 so K moved up 51
3656
-5
36/48 as D/12 so D moved up 9
9
12
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
L2L1 L1 L2 L2 L2 L3 L3
y3y5
y4
y3 = 3(L1)/2y4 = 3(L2)/4y5 = (L3)/2
ILMD
3L2
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILMB
128 8 12 12 12 10 10
48/48 = left end/16 so LE moved down 16
48
16
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILMB
4L2
y6
y6= 2L1
L2L1 L1 L2 L2 L2 L3 L3
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILRB
128 8 12 12 12 10 10
1/48 = left end/64 so LE moved up 1.333
1/48 = right end/20 so K moved down 0.417
-0.4166
1.0
1.333
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
128 8 12 12 12 10 10
48
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILRB
y8
1.0
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
48
y7
y7 = (4L2+2L1)*(1/(4*L2))y8 = 2*L3*(1/(4*L2))
L2L1 L1 L2 L2 L2 L3 L3
12
CA B D E F H
8 8 12 12 12 10 10
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVC1.0
1.0
0.333
0.4167
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVC1.0
1.0
y9
y10
y9 = L1/2L2y10 = -L3/2L2
L2L1 L1 L2 L2 L2 L3 L3
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILVH
128 8 12 12 12 10 10
1.0
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILMF
128 8 12 12 12 10 10
12 32
-15-4
9
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
L2L1 L1 L2 L2 L2 L3 L3
y11
y12
y13
y11 =L1/2 y12 = (3/4)L2y13 = (3/2)*(L3)
ILMF
L2
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILMH
128 8 12 12 12 10 10
48
16=20
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
Y14 = -2L3
ILMH
L2L1 L1 L2 L2 L2 L3 L3
y14
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
ILRG
128 8 12 12 12 10 10
1.0
1.417
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
128 8 12 12 12 10 10
0.333
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
1.0
y16
CA B D E F H
NOT TO SCALE B and G are to immediate left of supports C and H are to immediate right of supports
JG K
L2L1 L1 L2 L2 L2 L3 L3
ILRGy15
y16 = (4*L2+2*L3)/(4*L2)
Y15 = -(2L1)/(4*L2)