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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
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 -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 AB= 0 Knm FEM BC= fem(nf)-0.5fem(fn)
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(fn)= wL2/12= 20.83333 kNm FEM BC= 9 Knm
FEM BA= -31.25 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))= 0.4736842DF(BC)=(KbC/(Kba+Kbc))= 0.5263158DF(CB)= 1
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 AB= 0 Knm FEM BC= fem(nf)-0.5fem(fn)
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(fn)= wL2/12= 20.83333 kNm FEM BC= 9 Knm
FEM BA= -31.25 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))= 0.4736842DF(BC)=(KbC/(Kba+Kbc))= 0.5263158DF(CB)= 1
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
JOINT A B CMEMBER AB BA BC CB
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
JOINT A B CMEMBER AB BA BC CB
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
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
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 23 -17 DF BA = Kab/(Kab+Kbc)= 0.7DF 0 0.666667 0.333333 0 DF Bc = Kcb/(Kab+Kbc)= 0.3
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
AB 0 3EI/L 0.461538 1BA 0 3EI/L 0.461538 0.3658537BC 0 4EI/L 0.8 0.6341463CB 0 4EI/L 0.8 0.6341463CD 0 3EI/L 0.461538 0.3658537DC 0 3EI/L 0.461538 1
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
WITHOUT SIDES WAYL DF
AB 0 3EI/L 0.46154 1BA 0 3EI/L 0.46154 0.365854BC 0 4EI/L 0.8 0.634146CB 0 4EI/L 0.8 0.634146CD 0 3EI/L 0.46154 0.365854DC 0 3EI/L 0.46154 1
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
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
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
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
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
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