MFYLI
4
LINEAS DE INFLUENCIA DE LA VIGA a b RA RB (m) (m) (Tn) (Tn) 0.00 6.00 10.00 0.00 0.60 5.40 9.28 0.39 1.20 4.80 8.49 0.92 1.80 4.20 7.62 1.63 2.40 3.60 6.65 2.56 3.00 3.00 5.57 3.76 3.60 2.40 4.36 5.22 4.20 1.80 3.06 6.87 4.80 1.20 1.78 8.49 5.40 0.60 0.69 9.68 6.00 0.00 0.00 10.00 A. PARA LAS REACCIONES a b RA RB (m) (m) (Tn) (Tn) 11.00 -1.00 12.22 -15.44 12.00 -2.00 12.91 -17.81 13.00 -3.00 13.59 -20.19 14.00 -4.00 14.28 -22.56 15.00 -5.00 14.97 -24.94 16.00 -6.00 15.66 -27.32 17.00 -7.00 16.35 -29.69 18.00 -8.00 17.03 -32.07 19.00 -9.00 17.72 -34.44 0.00 0.60 1.20 1.80 2.40 3.00 3.60 0.00 2.00 4.00 6.00 8.00 10.00 12.00 a RA 10.00 12.00 _= ( _2 ) [ 〖 2 〗 ^2 ( − )− 〖 _1 〗 ^2 (2 _1−3 )+ ^ (2−3 )+2 〖〖 _1 〗 _2 〗 ^2 ]/2[ ^3 〖 ( _ 2) 〗 ^2 + 〖〖 _1 〗 ^2 ( − ) 〗 ^3 ] _=−/ −( ( _2 ) _1 [ 〖 2 〗 ^2 ( − )− 〖 _1 〗 ^2 +2 _1 〖 _2 〗 ^3)/2[ ^3 ( _ 2 )^2 + 〖〖 _1 〗 ^2 ( − _ = / −( ( _2 ) _1 [ 〖 2 〗 ^2 ( − )− 〖 _1 〗 ^2 ( (2 +3 )]+2 _1 〖 _2 〗 ^3)/2[ ^3 ( _ 2 )^2 + 〖〖 _1 ( − ) 〗 ^3 ]
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Transcript of MFYLI
LINEAS DE INFLUENCIA DE LA VIGA
a b RA RB RC(m) (m) (Tn) (Tn) (Tn)0.00 6.00 10.00 0.00 0.000.60 5.40 9.28 0.39 0.331.20 4.80 8.49 0.92 0.591.80 4.20 7.62 1.63 0.752.40 3.60 6.65 2.56 0.783.00 3.00 5.57 3.76 0.683.60 2.40 4.36 5.22 0.434.20 1.80 3.06 6.87 0.074.80 1.20 1.78 8.49 -0.275.40 0.60 0.69 9.68 -0.376.00 0.00 0.00 10.00 0.00
A. PARA LAS REACCIONES
a b RA RB RC(m) (m) (Tn) (Tn) (Tn)
11.00 -1.00 12.22 -15.44 13.2212.00 -2.00 12.91 -17.81 14.9113.00 -3.00 13.59 -20.19 16.5914.00 -4.00 14.28 -22.56 18.2815.00 -5.00 14.97 -24.94 19.9716.00 -6.00 15.66 -27.32 21.6617.00 -7.00 16.35 -29.69 23.3518.00 -8.00 17.03 -32.07 25.0319.00 -9.00 17.72 -34.44 26.72
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RA
a
RA
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RB
a
RB
𝑹_𝑩= (𝑃𝑎 _2 )𝐿 [〖 2𝑎〗 ^2 ( −𝐿 )−𝑎 〖𝐿 _1〗 ^2 (2 _1−3 )𝐿 𝐿+ ^2 (2𝑎 𝑎−3 )+2𝐿 〖〖𝐿 _1 𝐿〗 _2〗 ^2 ]/2[ ^3𝑎 〖 ( _𝐿 2)〗 ^2 + 〖〖𝐿 _1〗 ^2 ( −𝐿 𝑎)〗 ^3 ]
𝑹_𝑨=𝑃−𝑃𝑎/𝐿 −( (𝑃𝑎 _2 ) _1𝐿 𝐿 [〖 2𝑎〗 ^2 ( −𝐿 )−𝑎 〖𝐿 _1〗 ^2 (2 _1−3 )+ ^2 𝐿 𝐿 𝑎(2 +3 )]+2 _1 𝑎 𝐿 𝑃𝑎𝐿 〖𝐿 _2〗 ^3)/2𝐿[ ^3𝑎 ( _𝐿 2 )^2 + 〖〖𝐿 _1〗 ^2 ( −𝐿 𝑎)〗 ^3 ] ∗[ +1]𝐿
𝑹_𝑪=𝑃𝑎/𝐿 −( (𝑃𝑎 _2 ) _1𝐿 𝐿 [〖 2𝑎〗 ^2 ( −𝐿 )−𝑎 〖𝐿 _1〗 ^2 (2 _1−3 )𝐿 𝐿+ ^2 (2 +3 )]+2 _1 𝑎 𝑎 𝐿 𝑃𝑎𝐿 〖𝐿 _2〗 ^3)/2𝐿[ ^3𝑎 ( _𝐿 2 )^2 + 〖〖𝐿 _1〗 ^2 ( −𝐿 𝑎)〗 ^3 ]
20.00 -10.00 18.41 -36.82 28.4121.00 -11.00 19.10 -39.19 30.10
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RA
a
RA
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RB
a
RB
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00
-0.60-0.40-0.200.000.200.400.600.801.00
LINEA DE INFLUENCIA PARA RC
a
RC
Evaluamos:L 1 = 6.00 mL2 = 5.00 mP = 10.00 Tn
Evaluamos:L 1 = 10.00L2 = 10.00P = 10.00
Donde:
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RA
a
RA
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RB
a
RB
𝑹_𝑨=𝑃−𝑃𝑎/𝐿 −( (𝑃𝑎 _2 ) _1𝐿 𝐿 [〖 2𝑎〗 ^2 ( −𝐿 )−𝑎 〖𝐿 _1〗 ^2 (2 _1−3 )+ ^2 𝐿 𝐿 𝑎(2 +3 )]+2 _1 𝑎 𝐿 𝑃𝑎𝐿 〖𝐿 _2〗 ^3)/2𝐿[ ^3𝑎 ( _𝐿 2 )^2 + 〖〖𝐿 _1〗 ^2 ( −𝐿 𝑎)〗 ^3 ] ∗[ +1]𝐿
𝑹_𝑪=𝑃𝑎/𝐿 −( (𝑃𝑎 _2 ) _1𝐿 𝐿 [〖 2𝑎〗 ^2 ( −𝐿 )−𝑎 〖𝐿 _1〗 ^2 (2 _1−3 )𝐿 𝐿+ ^2 (2 +3 )]+2 _1 𝑎 𝑎 𝐿 𝑃𝑎𝐿 〖𝐿 _2〗 ^3)/2𝐿[ ^3𝑎 ( _𝐿 2 )^2 + 〖〖𝐿 _1〗 ^2 ( −𝐿 𝑎)〗 ^3 ]
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RA
a
RA
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.000.00
2.00
4.00
6.00
8.00
10.00
12.00
LINEA DE INFLUENCIA PARA RB
a
RB
0.00 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00
-0.60-0.40-0.200.000.200.400.600.801.00
LINEA DE INFLUENCIA PARA RC
a
RC
