cven 345 quiz b problem 1 l1 l2 r1 p r2 l1 l2...l1 l2 l3 l1 l2 l3 m2=1*l3 m1=1*l3 m1=1*l3...

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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 L2 L3 L1 L2 L3 1*L3 1*L3 1*L3 1*(L1+L2) 1*L2 Required moment diagram shapes Values vary by student exam

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Page 1: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 2: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 3: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 4: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 5: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 6: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 7: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 8: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 9: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 10: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 11: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 12: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 13: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 14: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 15: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 16: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 17: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 18: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 19: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 20: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 21: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 22: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 23: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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

Page 24: CVEN 345 Quiz B Problem 1 L1 L2 R1 P R2 L1 L2...L1 L2 L3 L1 L2 L3 m2=1*L3 m1=1*L3 m1=1*L3 m3=1*(L1+L2) M0 M1 = - P*L1 L1 L2 L3 m4=1*L2 P DeltaLittle11 = Integral(m1*m1*dx)/EI Volume

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)