mdm program

ROLLER ROLLER12 kN/m

8 kN/m

HINGED5 m 6 m

FEM AB= 0 Knm FEM BC= fem(nf)-0.5fem(fn)

FEM BA= fem(nf)-0.5fem(fn) fem(nf)= wL2/12=

fem(nf)= wL2/12= -16.6666667 kNm fem(fn)= wL2/12=

fem(fn)= wL2/12= 16.6666667 kNm FEM BC= 54 Knm

FEM BA= -25 Knm FEM CB= 0 Knm

K(AB)=K(BA)=3EI/L 0.45K(BC)=K(CB)=3EI/L 0.5

DF(AB)= 1DF(BA)=(KbA/(Kba+Kbc))= 0.47368421DF(BC)=(KbC/(Kba+Kbc))= 0.52631579DF(CB)= 1

JOINT A B CMEMBER AB BA BC CB

FEM 0 -25 54 0IST DIST 0 -13.736842 -15.2631579 0

COM 0 0 0 02ND DIST 0 0 0 0

SUM 0 -38.736842 38.7368421 0

ANSWERS

Determine the internal moment in the beam at B then draw the moment diagram. Assume C is a pin. Segmant AB has a moment of inertia of

I(AB)=0.75 I(BC). Ei is constant

𝐸𝐼0.75𝐸𝐼��

𝐵 𝐶

ROLLER ROLLER2 kN/m

10 kN/m

5 m 6

FEM AB= 0 Knm

36 kNm FEM BA= fem(nf)-0.5fem(fn)

-36 kNm fem(nf)= wL2/12= -20.8333333 kNm

fem(fn)= wL2/12= 20.8333333 kNm

FEM BA= -31.25 Knm




FEM 0 -31.25 9 0IST DIST 0 10.53947368 11.7105263 0

COM 0 0 0 02ND DIST 0 0 0 0

SUM 0 -20.7105263 20.7105263 0

Determine the internal moment in the beam at B then draw the moment diagram. Assume C is a pin. Segmant AB has a moment of inertia

of I(AB)=0.75 I(BC). Ei is constant

𝐸𝐼0.75𝐸𝐼𝐴 𝐵

HINGEDm

FEM BC= fem(nf)-0.5fem(fn)

fem(nf)= wL2/12= 6 kNm

fem(fn)= wL2/12= -6 kNm

FEM BC= 9 Knm

FEM CB= 0 Knm

ANSWERS

𝐶

ROLLER ROLLER2 kN/m

10 kN/m

HINGED5 m 6 m


FEM BA= fem(nf)-0.5fem(fn) fem(nf)= wL2/12= 6 kNm

fem(nf)= wL2/12= -20.83333 kNm fem(fn)= wL2/12= -6 kNm


FEM BA= -31.25 Knm FEM CB= 0 Knm



JOINT A CMEMBER AB BA BC CB

FEM 0 -31.25 9 0IST DIST 0 10.539474 11.710526 0

COM 0 0 0 02ND DIST 0 0 0 0

SUM 0 -20.71053 20.710526 0

ANSWERS

Determine the internal moment in the beam at B

then draw the moment diagram. Assume C is a pin.

Segmant AB has a moment of inertia of I(AB)=0.75

I(BC). Ei is constant

B

ܧܫ0.75ܧܫ

ܣ ܤ ܥ

ROLLER ROLLER2 kN/m

10 kN/m

HINGED5 m 6 m


FEM BA= fem(nf)-0.5fem(fn) fem(nf)= wL2/12= 6 kNm

fem(nf)= wL2/12= -20.83333 kNm fem(fn)= wL2/12= -6 kNm


FEM BA= -31.25 Knm FEM CB= 0 Knm



JOINT A CMEMBER AB BA BC CB

FEM 0 -31.25 9 0IST DIST 0 10.539474 11.710526 0

COM 0 0 0 02ND DIST 0 0 0 0

SUM 0 -20.71053 20.710526 0

ANSWERS

Determine the internal moment in the beam at B

then draw the moment diagram. Assume C is a pin.

Segmant AB has a moment of inertia of I(AB)=0.75

I(BC). Ei is constant

B

ܧܫ0.75ܧܫ

ܣ ܤ ܥ

FIXED ROLLER 8 8 8

4 2 2 2 2


FEM 0 0 20 -20DF 0 0.66666667 0.33333333 0

IST DIST 0 -13.333333 -6.6666667 0COM -6.6666667 0 0 -3.3333333DF 0 0.66666667 0.33333333 0

2ND DIST 0 0 0 0

SUM -6.6666667 -13.333333 13.3333333 -23.333333

FIXED ROLLER 10 11 2

4 2 2 2 2


FEM 0 0 23 -17DF 0 0.66666667 0.33333333 0

��

𝐵 𝐶

��

𝐵 𝐶��

IST DIST 0 -15.333333 -7.6666667 0COM -7.6666667 0 0 -3.8333333DF 0 0.66666667 0.33333333 0

2ND DIST 0 0 0 0

SUM -7.6666667 -15.333333 15.3333333 -20.833333

FEM AB= 0 KnmFIXED FEM BA = 0 Knm

FEM BC = 15PL/48FEM BC = 9 + 8 + 3FEM BC = 20 KnmFEM CB = -9 + -8 + -3

FEM CB = -20 Knm

K AB = K BA = 4EI/L = 1

K BC = K CB = 4EI/L = 0.5

DF AB = 0DF BA = Kab/(Kab+Kbc)= 0.67DF Bc = Kcb/(Kab+Kbc)= 0.33

DF CB= 0

FEM AB= 0 KnmFIXED FEM BA = 0 Knm

FEM BC = 15PL/48FEM BC = 11.25 + 11 + 0.75FEM BC = 23 KnmFEM CB = -2.25 + -11 + -3.8

FEM CB = -17 Knm

K AB = K BA = 4EI/L = 1

K BC = K CB = 4EI/L = 0.5

DF AB = 0DF BA = Kab/(Kab+Kbc)= 0.67DF Bc = Kcb/(Kab+Kbc)= 0.33

𝐶

𝐶

FEM AB= 0 Knm

FIXED ROLLER 8 8 8 FIXED FEM BA = 0 KnmFEM BC = 15PL/48FEM BC = 9 + 8 + 3FEM BC = 20 Knm

2 2 2 2 FEM CB = -9 + -8 + -3FEM CB = -20 Knm

K AB = K BA = 4EI/L = 1K BC = K CB = 4EI/L = 0.5

JOINT A CMEMBER AB BA BC CB DF AB = 0

FEM 0 0 20 -20 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3

IST DIST 0 -13.3333 -6.66667 0 DF CB= 0

COM -6.66667 0 0 -3.33333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -6.66667 -13.3333 13.33333 -23.3333

4

B

ܣ ܤ ܥ

FEM AB= 0 Knm

FIXED ROLLER 10 11 2 FIXED FEM BA = 0 KnmFEM BC = 15PL/48FEM BC = 11.25 + 11 + 0.8FEM BC = 23 Knm

2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

DF CB= 0

FEM AB= 0 Knm


2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -9 + -8 + -3FEM CB = -20 Knm




IST DIST 0 -13.3333 -6.66667 0 DF CB= 0

COM -6.66667 0 0 -3.33333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -6.66667 -13.3333 13.33333 -23.3333

4

B

ܣ ܤ ܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -9 + -8 + -3FEM CB = -20 Knm




IST DIST 0 -13.3333 -6.66667 0 DF CB= 0

COM -6.66667 0 0 -3.33333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -6.66667 -13.3333 13.33333 -23.3333

4

B

ܣ ܤ ܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

FEM AB= 0 Knm


2 2 2 2 FEM CB = -2.25 + -11 + -4FEM CB = -17 Knm




IST DIST 0 -15.3333 -7.66667 0 DF CB= 0

COM -7.66667 0 0 -3.83333DF 0 0.666667 0.333333 0

2ND DIST 0 0 0 0SUM -7.66667 -15.3333 15.33333 -20.8333

4

B

ܣ ܤ ܣܥ

C

20

1 4

PIN CONNECTED 12 PIN CONNECTED

2.5 5 2.5

WITHOUT SIDES WAYL K DF FEM

AB 12.25765 3EI/L 0.244745 1 0BA 12.25765 3EI/L 0.244745 0.234263 0BC 5 4EI/L 0.8 0.765737 Pab^2/L^2 12.8CB 5 4EI/L 0.8 0.765737 Pab^2/L^3 -3.2CD 12.25765 3EI/L 0.244745 0.234263 0DC 12.25765 3EI/L 0.244745 1 0

MoA B C D

MEMBER AB BA BC CB CD DCFEM 0 0 12.8 -3.2 0 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 -2.99857 -9.80143 2.450358 0.7496415 0CO 0 1.225179 -4.90072 0

DIST 0 -0.28701 -0.93817 3.75266 1.1480566 0CO 0 1.87633 -0.46908 0

DIST 0 -0.43955 -1.43678 0.359194 0.1098887 0CO 0 0.179597 -0.71839 0

DIST 0 -0.04207 -0.13752 0.550096 0.1682917 0CO 0 0.275048 -0.06876 0

DIST 0 -0.06443 -0.21061 0.052654 0.0161084 0CO 0 0.026327 -0.10531 0

DIST 0 -0.00617 -0.02016 0.080638 0.0246696 0SUM 0 -3.83781 3.837809 -2.21666 2.2166564 0

WITH SIDES WAY

∆ AB = 1.021471 ∆'

��

𝐵 𝐶

��

∆ BC = 0.416667 ∆'∆ CD = 1.021471 ∆'

LET FEM AB = 100KNM100= 6EI∆ AB/L^2100= 0.020395 EI∆EI∆= 4903.06FEM BC= -490.306 KNMFEM DC= 100 KNMFEM AB= 100 KNM

WITHOUT SIDES WAYL K DF

AB 0 3EI/L 0.244745 1BA 0 3EI/L 0.244745 0.234263BC 0 4EI/L 0.8 0.765737CB 0 4EI/L 0.8 0.765737CD 0 3EI/L 0.244745 0.234263DC 0 3EI/L 0.244745 1

M'A B C D

MEMBER AB BA BC CB CD DCFEM 0 100 -490.306 -490.306 100 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 91.43425 298.8718 298.8718 91.434254 0CO 0 149.4359 149.4359 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 -35.0073 -114.429 -114.429 -35.0073 0CO 0 -57.2143 -57.2143 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 13.40319 43.8111 43.8111 13.403191 0CO 0 21.90555 21.90555 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 -5.13166 -16.7739 -16.7739 -5.13166 0CO 0 -8.38695 -8.38695 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 1.964751 6.422195 6.422195 1.964751 0CO 0 3.211097 3.211097 0DF 1 0.234263 0.765737 0.765737 0.234263 1

DIST 0 -0.75224 -2.45886 -2.45886 -0.752241 0SUM 0 165.911 -165.911 -165.911 165.911 0

M=Mo+(R/R')M'

A B C DMEMBER AB BA BC CB CD DCMo 0 -3.83781 3.837809 -2.21666 2.2166564 0R/R' 0.050091 0.050091 0.050091 0.050091 0.0500906 0.050091M' 0 165.911 -165.911 -165.911 165.911 0M 0 4.472767 -4.47277 -10.5272 10.527233 0ANSWER

PIN CONNECTED

20

1 43.837809 -2.21666 R

516.32423 3.67577

-3.83781 2.216656

12

3.720699 2.5 2.5 -0.95051

16.32423 3.67577

R= 2.770192

1 4-165.911 -165.911 R'

5-66.3644 66.3644

165.911 165.911

12

-27.6518 2.5 2.5 -27.6518

-66.3644 66.3644

R'= 55.30367

C

10

1 4

6 PIN CONNECTED PIN CONNECTED

2.5 5 2.5

WITHOUT SIDES WAYL K DF FEM

AB 6.5 3EI/L 0.461538 1 0BA 6.5 3EI/L 0.461538 0.3658537 0BC 5 4EI/L 0.8 0.6341463Pab^2/L^2 6.4CB 5 4EI/L 0.8 0.6341463Pab^2/L^3 -1.6CD 6.5 3EI/L 0.461538 0.3658537 0DC 6.5 3EI/L 0.461538 1 0

MoA B C D

MEMBER AB BA BC CB CD DCFEM 0 0 6.4 -1.6 0 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 -2.34146 -4.05854 1.0146341 0.585366 0CO 0 0.507317 -2.0292683 0

DIST 0 -0.1856 -0.32171 1.2868531 0.742415 0CO 0 0.643427 -0.1608566 0

DIST 0 -0.2354 -0.40803 0.1020066 0.05885 0CO 0 0.051003 -0.2040133 0

DIST 0 -0.01866 -0.03234 0.1293743 0.074639 0CO 0 0.064687 -0.0161718 0

DIST 0 -0.02367 -0.04102 0.0102553 0.005917 0CO 0 0.005128 -0.0205106 0

DIST 0 -0.00188 -0.00325 0.0130067 0.007504 0SUM 0 -2.80667 2.806669 -1.4746904 1.47469 0

WITH SIDES WAY

∆ AB = 1.083333 ∆'

��

𝐵 𝐶

��

∆ BC = 0.833333 ∆'∆ CD = 1.083333 ∆'

LET FEM AB = 100KNM100= 6EI∆ AB/L^2100= 0.076923 EI∆EI∆= 1300FEM BC= -260 KNMFEM DC= 100 KNMFEM AB= 100 KNM

WITHOUT SIDES WAYL K DF


M'A B C D

MEMBER AB BA BC CB CD DCFEM 0 100 -260 -260 100 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 58.53659 101.4634 101.46341 58.53659 0CO 0 50.73171 50.731707 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 -18.5604 -32.1713 -32.171327 -18.5604 0CO 0 -16.0857 -16.085663 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 5.884999 10.20066 10.200665 5.884999 0CO 0 5.100332 5.1003323 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 -1.86598 -3.23436 -3.234357 -1.86598 0CO 0 -1.61718 -1.6171785 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 0.591651 1.025528 1.0255278 0.591651 0CO 0 0.512764 0.5127639 0DF 1 0.365854 0.634146 0.6341463 0.365854 1

DIST 0 -0.1876 -0.32517 -0.3251674 -0.1876 0SUM 0 144.3993 -144.399 -144.39928 144.3993 0

M=Mo+(R/R')M'

A B C DMEMBER AB BA BC CB CD DCMo 0 -2.80667 2.806669 -1.4746904 1.47469 0R/R' 0.030582 0.030582 0.030582 0.0305818 0.030582 0.030582M' 0 144.3993 -144.399 -144.39928 144.3993 0M 0 1.60932 -1.60932 -5.8906797 5.89068 0ANSWER

WITHOUT SIDES WAYL DF

AB 6.5 3EI/L 0.46154 1 0BA 6.5 3EI/L 0.46154 0.365854 0BC 5 4EI/L 0.8 0.634146 Pab 2̂/L 2̂ 6.4CB 5 4EI/L 0.8 0.634146 Pab 2̂/L 3̂ -1.6CD 6.5 3EI/L 0.46154 0.365854 0 10DC 6.5 3EI/L 0.46154 1 0

1 42.80667 -1.4747 R

A D 5MEMBER AB BA BC CB CD DC 8.2664 1.7336

FEM 0 0 6.4 -1.6 0 0DF 1 0.36585 0.63415 0.634146 0.36585 1 -2.8067 1.47469

DIST 0 -2.3415 -4.0585 1.014634 0.58537 0CO 0 0.50732 -2.02927 0

DIST 0 -0.1856 -0.3217 1.286853 0.74242 0CO 0 0.64343 -0.16086 0

DIST 0 -0.2354 -0.408 0.102007 0.05885 0 6CO 0 0.051 -0.20401 0

DIST 0 -0.0187 -0.0323 0.129374 0.07464 0CO 0 0.06469 -0.01617 0 3.91211 2.5 2.5 -0.9681

DIST 0 -0.0237 -0.041 0.010255 0.00592 0CO 0 0.00513 -0.02051 0 8.2664 1.7336

DIST 0 -0.0019 -0.0033 0.013007 0.0075 0SUM 0 -2.8067 2.80667 -1.47469 1.47469 0 R= 2.94399

WITH SIDES WAY

∆ AB = 1.08333 ∆'∆ BC = 0.83333 ∆'∆ CD = 1.08333 ∆'

LET FEM AB = 100KNM100= 6EI∆ AB/L 2̂100= 0.07692 EI∆EI∆= 1300FEM BC= -260 KNMFEM DC= 100 KNMFEM AB= 100 KNM



1 4-144.4 -144.4 R'

A D 5MEMBER AB BA BC CB CD DC -57.76 57.7597

FEM 0 100 -260 -260 100 0DF 1 0.36585 0.63415 0.634146 0.36585 1 144.399 144.399

DIST 0 58.5366 101.463 101.4634 58.5366 0CO 0 50.7317 50.73171 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -18.56 -32.171 -32.1713 -18.56 0CO 0 -16.086 -16.0857 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 5.885 10.2007 10.20066 5.885 0 6CO 0 5.10033 5.100332 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -1.866 -3.2344 -3.23436 -1.866 0CO 0 -1.6172 -1.61718 0 -48.133 2.5 2.5 -48.133DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 0.59165 1.02553 1.025528 0.59165 0CO 0 0.51276 0.512764 0 -57.76 57.7597DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -0.1876 -0.3252 -0.32517 -0.1876 0SUM 0 144.399 -144.4 -144.399 144.399 0 R'= 96.2662

M=Mo+(R/R')M'

A DMEMBER AB BA BC CB CD DCMo 0 -2.8067 2.80667 -1.47469 1.47469 0R/R' 0.03058 0.03058 0.03058 0.030582 0.03058 0.03058M' 0 144.399 -144.4 -144.399 144.399 0M 0 1.60932 -1.6093 -5.89068 5.89068 0 ANSWER

K FEM

MoB C

B C

K

M'B C



1 42.80667 -1.4747 R


FEM 0 0 6.4 -1.6 0 0DF 1 0.36585 0.63415 0.634146 0.36585 1 -2.8067 1.47469

DIST 0 -2.3415 -4.0585 1.014634 0.58537 0CO 0 0.50732 -2.02927 0

DIST 0 -0.1856 -0.3217 1.286853 0.74242 0CO 0 0.64343 -0.16086 0

DIST 0 -0.2354 -0.408 0.102007 0.05885 0 6CO 0 0.051 -0.20401 0

DIST 0 -0.0187 -0.0323 0.129374 0.07464 0CO 0 0.06469 -0.01617 0 3.91211 2.5 2.5 -0.9681

DIST 0 -0.0237 -0.041 0.010255 0.00592 0CO 0 0.00513 -0.02051 0 8.2664 1.7336

DIST 0 -0.0019 -0.0033 0.013007 0.0075 0SUM 0 -2.8067 2.80667 -1.47469 1.47469 0 R= 2.94399

WITH SIDES WAY

∆ AB = 1.08333 ∆'∆ BC = 0.83333 ∆'∆ CD = 1.08333 ∆'




1 4-144.4 -144.4 R'


FEM 0 100 -260 -260 100 0DF 1 0.36585 0.63415 0.634146 0.36585 1 144.399 144.399

DIST 0 58.5366 101.463 101.4634 58.5366 0CO 0 50.7317 50.73171 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -18.56 -32.171 -32.1713 -18.56 0CO 0 -16.086 -16.0857 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 5.885 10.2007 10.20066 5.885 0 6CO 0 5.10033 5.100332 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -1.866 -3.2344 -3.23436 -1.866 0CO 0 -1.6172 -1.61718 0 -48.133 2.5 2.5 -48.133DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 0.59165 1.02553 1.025528 0.59165 0CO 0 0.51276 0.512764 0 -57.76 57.7597DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -0.1876 -0.3252 -0.32517 -0.1876 0SUM 0 144.399 -144.4 -144.399 144.399 0 R'= 96.2662

M=Mo+(R/R')M'


K FEM

MoB C

B C

K

M'B C

PIN CONNECTED

10

1 42.806669 -1.47469 R

58.266396 1.733604

-2.80667 1.47469

6

3.91211 2.5 2.5 -0.96812

8.266396 1.733604

R= 2.943993

1 4-144.399 -144.399 R'

5-57.7597 57.75971

144.3993 144.3993

6

-48.1331 2.5 2.5 -48.1331

-57.7597 57.75971

R'= 96.26619



1 42.80667 -1.4747 R


FEM 0 0 6.4 -1.6 0 0DF 1 0.36585 0.63415 0.634146 0.36585 1 -2.8067 1.47469

DIST 0 -2.3415 -4.0585 1.014634 0.58537 0CO 0 0.50732 -2.02927 0

DIST 0 -0.1856 -0.3217 1.286853 0.74242 0CO 0 0.64343 -0.16086 0

DIST 0 -0.2354 -0.408 0.102007 0.05885 0 6CO 0 0.051 -0.20401 0

DIST 0 -0.0187 -0.0323 0.129374 0.07464 0CO 0 0.06469 -0.01617 0 3.91211 2.5 2.5 -0.9681

DIST 0 -0.0237 -0.041 0.010255 0.00592 0CO 0 0.00513 -0.02051 0 8.2664 1.7336

DIST 0 -0.0019 -0.0033 0.013007 0.0075 0SUM 0 -2.8067 2.80667 -1.47469 1.47469 0 R= 2.94399

WITH SIDES WAY

∆ AB = 1.08333 ∆'∆ BC = 0.83333 ∆'∆ CD = 1.08333 ∆'




1 4-144.4 -144.4 R'


FEM 0 100 -260 -260 100 0DF 1 0.36585 0.63415 0.634146 0.36585 1 144.399 144.399

DIST 0 58.5366 101.463 101.4634 58.5366 0CO 0 50.7317 50.73171 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -18.56 -32.171 -32.1713 -18.56 0CO 0 -16.086 -16.0857 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 5.885 10.2007 10.20066 5.885 0 6CO 0 5.10033 5.100332 0DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -1.866 -3.2344 -3.23436 -1.866 0CO 0 -1.6172 -1.61718 0 -48.133 2.5 2.5 -48.133DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 0.59165 1.02553 1.025528 0.59165 0CO 0 0.51276 0.512764 0 -57.76 57.7597DF 1 0.36585 0.63415 0.634146 0.36585 1

DIST 0 -0.1876 -0.3252 -0.32517 -0.1876 0SUM 0 144.399 -144.4 -144.399 144.399 0 R'= 96.2662

M=Mo+(R/R')M'


K FEM

MoB C

B C

K

M'B C

PINNED 36 Kn/M

2 6

4

PINNED PINNED

MEMBER LENGTH E(GPA) I(10^6MM4) K

AB 2 200 320 3EI/L=

BC 6 200 320 4EI/L=

BD 4 200 240 3EI/L=

CE 4 200 400 3EI/L=

FEM AB 12 Knm

FEM BA -12 Knm

FEM BC 108 Knm

FEM CB -108 Knm

FEM CE 30 KNM

FEM EC -30 KNM

FEM BD 0 KNM

FEM DB 0 KNM

JOINT A B

MEMBER AB BA BD BC

K 96000 96000 36000 42666.6666666667

FEM 12 -12 0 108

DF 1 0.54961832061 0.2061068702 0.24427480916031

DIST -12 -52.763358779 -19.786259542 -23.450381679389

CO 0 -6 0 16.2077922077922

DIST 0 -5.6103896104 -2.1038961039 -2.4935064935065

CO 0 0 -0.680479825518

DIST 0 0.37400417891 0.1402515671 0.16622407951585

CO 0 0 0.25906560971496

��

𝐵 𝐶

��

DIST 0 -0.1423872053 -0.053395202 -0.0632832023731

CO 0 0 -0.0172700342354

DIST 0 0.00949192721 0.0035594727 0.00421863431705

SUM 0 -76.132639488 -21.799739808 97.9323792963177

2 2

60 KN

2

K MEMBER

96000 AB

42666.6666666667 BC

36000 BD

60000 CE

FEM AB

FEM BA

FEM BC

FEM CB

FEM CE

FEM EC

FEM BD

FEM DB

C E D JOINT

CB CE EC DB MEMBER

42666.6666666667 60000 60000 1 K

-108 30 -30 0 FEM

0.41558441558442 0.58441558442 1 1 DF

32.4155844155844 45.5844155844 30 0 DIST

-11.725190839695 15 CO

-1.360959651036 -1.9138495093 0 0 DIST

-1.2467532467532 0 CO

0.51813121942992 0.72862202732 0 0 DIST

0.08311203975792 0 CO

𝐶

𝐸

�� 𝐵

-0.0345400684708 -0.0485719713 0 0 DIST

-0.0316416011866 0 CO

0.01314975633727 0.01849184485 0 0 DIST

-89.369107976032 89.369107976 0 0 SUM

PINNED 10 Kn/M

6 2

4 7 KN

PINNED PINNED 2

LENGTH E(GPA) I(10^6MM4) K

2 200 320 3EI/L= 96000

6 200 320 4EI/L= 42666.6666666667

4 200 240 3EI/L= 36000

4 200 400 3EI/L= 60000

3.33333333333 Knm

-3.3333333333 Knm

30 Knm

-30 Knm

3.5 KNM

-3.5 KNM

0 KNM

0 KNM

A B C E

AB BA BD BC CB CE EC

96000 96000 36000 42666.6666666667 42666.6666666667 60000 60000

3.33333333333 -3.3333333333 0 30 -30 3.5 -3.5

1 0.54961832061 0.20610687023 0.24427480916031 0.41558441558442 0.58441558442 1

-3.3333333333 -14.65648855 -5.4961832061 -6.5139949109415 11.012987012987 15.487012987 3.5

0 -1.6666666667 0 5.50649350649351 -3.2569974554707 1.75

0 -2.1104391791 -0.7914146922 -0.9379729685073 0.62628465681901 0.88071279865 0

0 0 0.3131423284095 -0.4689864842537 0

0 -0.1721087607 -0.0645407852 -0.0764927825122 0.19490347397555 0.27408301028 0

0 0 0.09745173698777 -0.0382463912561 0

𝐵 𝐶

�� 𝐸

FEM AB 3.33333333 Knm

FEM BA -3.33333333 Knm

FEM BC 30 Knm

FEM CB -30 Knm

FEM CE 3.5 KNM

FEM EC -3.5 KNM

FEM BD 0 KNM

FEM DB 0 KNM

0 -0.05356126 -0.0200854725 -0.023805004455 0.01589460415839 0.0223517871 0

0 0 0.00794730207919 -0.0119025022275 0

0 -0.0043679828 -0.0016379936 -0.0019413256987 0.00494649443221 0.0069560078 0

0 -21.996965732 -6.3738621496 28.3708278818552 -21.921116590836 21.9211165908 0

D

DB

1

0

1

0

0

0

MEMBER LENGTH E(GPA) I(10^6MM4)

AB 2 200 320 3EI/L= 96000

BC 6 200 320 4EI/L= 42666.66667

BD 4 200 240 3EI/L= 36000

CE 4 200 400 3EI/L= 60000

K

FEM AB 3.33333333 Knm

FEM BA -3.33333333 Knm

FEM BC 30 Knm

FEM CB -30 Knm

FEM CE 3.5 KNM

FEM EC -3.5 KNM

FEM BD 0 KNM

FEM DB 0 KNM

JOINT A E D

MEMBER AB BA BD BC CB CE EC DB

K 96000 96000 36000 42666.66667 42666.66667 60000 60000 1

FEM 3.33333333 -3.33333333 0 30 -30 3.5 -3.5 0

DF 1 0.54961832 0.20610687 0.244274809 0.415584416 0.58441558 1 1

DIST -3.33333333 -14.6564885 -5.49618321 -6.513994911 11.01298701 15.487013 3.5 0

CO 0 -1.66666667 0 5.506493506 -3.256997455 1.75

DIST 0 -2.11043918 -0.79141469 -0.937972969 0.626284657 0.8807128 0 0

CO 0 0 0.313142328 -0.468986484 0

DIST 0 -0.17210876 -0.06454079 -0.076492783 0.194903474 0.27408301 0 0

CO 0 0 0.097451737 -0.038246391 0

DIST 0 -0.05356126 -0.02008547 -0.023805004 0.015894604 0.02235179 0 0

CO 0 0 0.007947302 -0.011902502 0

DIST 0 -0.00436798 -0.00163799 -0.001941326 0.004946494 0.00695601 0 0

SUM 0 -21.9969657 -6.37386215 28.37082788 -21.92111659 21.9211166 0 0

B C

0

0

0

JOINT A E D


K 96000 96000 36000 42666.66667 42666.66667 60000 60000 1

FEM 3.33333333 -3.33333333 0 30 -30 3.5 -3.5 0

DF 1 0.54961832 0.20610687 0.244274809 0.415584416 0.58441558 1 1

DIST -3.33333333 -14.6564885 -5.49618321 -6.513994911 11.01298701 15.487013 3.5 0

CO 0 -1.66666667 0 5.506493506 -3.256997455 1.75

DIST 0 -2.11043918 -0.79141469 -0.937972969 0.626284657 0.8807128 0 0

CO 0 0 0.313142328 -0.468986484 0

DIST 0 -0.17210876 -0.06454079 -0.076492783 0.194903474 0.27408301 0 0

CO 0 0 0.097451737 -0.038246391 0

DIST 0 -0.05356126 -0.02008547 -0.023805004 0.015894604 0.02235179 0 0

CO 0 0 0.007947302 -0.011902502 0

DIST 0 -0.00436798 -0.00163799 -0.001941326 0.004946494 0.00695601 0 0

SUM 0 -21.9969657 -6.37386215 28.37082788 -21.92111659 21.9211166 0 0

B C

MEMBER LENGTH E(GPA) I(10^6MM4)

AB 2 200 320 3EI/L= 96000

BC 6 200 320 4EI/L= 42666.66667

BD 4 200 240 3EI/L= 36000

CE 4 200 400 3EI/L= 60000

K

JOINT A E D


K 96000 96000 36000 42666.66667 42666.66667 60000 60000 1

FEM 3.33333333 -3.33333333 0 30 -30 3.5 -3.5 0

DF 1 0.54961832 0.20610687 0.244274809 0.415584416 0.58441558 1 1

DIST -3.33333333 -14.6564885 -5.49618321 -6.513994911 11.01298701 15.487013 3.5 0

CO 0 -1.66666667 0 5.506493506 -3.256997455 1.75

DIST 0 -2.11043918 -0.79141469 -0.937972969 0.626284657 0.8807128 0 0

CO 0 0 0.313142328 -0.468986484 0

DIST 0 -0.17210876 -0.06454079 -0.076492783 0.194903474 0.27408301 0 0

CO 0 0 0.097451737 -0.038246391 0

DIST 0 -0.05356126 -0.02008547 -0.023805004 0.015894604 0.02235179 0 0

CO 0 0 0.007947302 -0.011902502 0

DIST 0 -0.00436798 -0.00163799 -0.001941326 0.004946494 0.00695601 0 0

SUM 0 -21.9969657 -6.37386215 28.37082788 -21.92111659 21.9211166 0 0

B C

JOINT A E D


K 96000 96000 36000 42666.66667 42666.66667 60000 60000 1

FEM 3.33333333 -3.33333333 0 30 -30 3.5 -3.5 0

DF 1 0.54961832 0.20610687 0.244274809 0.415584416 0.58441558 1 1

DIST -3.33333333 -14.6564885 -5.49618321 -6.513994911 11.01298701 15.487013 3.5 0

CO 0 -1.66666667 0 5.506493506 -3.256997455 1.75

DIST 0 -2.11043918 -0.79141469 -0.937972969 0.626284657 0.8807128 0 0

CO 0 0 0.313142328 -0.468986484 0

DIST 0 -0.17210876 -0.06454079 -0.076492783 0.194903474 0.27408301 0 0

CO 0 0 0.097451737 -0.038246391 0

DIST 0 -0.05356126 -0.02008547 -0.023805004 0.015894604 0.02235179 0 0

CO 0 0 0.007947302 -0.011902502 0

DIST 0 -0.00436798 -0.00163799 -0.001941326 0.004946494 0.00695601 0 0

SUM 0 -21.9969657 -6.37386215 28.37082788 -21.92111659 21.9211166 0 0

B C

mdm program

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