Perhitungan Alinyemen Vertikal

3.6  Penentuan Alinyemen Vertikal

3.6.1        Vertikal Cembung PPV₁

Dikeahui data-data sebagai berikut:

·         Elevasi Sta A ( 35 + 550 )      = 888 m

·         Elevasi Sta B ( 35 + 600 )      = 888 m

·         Elevasi Sta C ( 35 + 650 )      = 879,75 m

·         V Rencana                              = 60 km/jam

            d₁         = ± ( Sta B – Sta A )

                        = ± (35 + 600 – 35 + 550 )

                        = 50 m

            d₂         = ± ( Sta C – Sta B )                                                                                                     = ± (35 + 650 – 35 + 600 )

                        = 50 m

            g₁            =

                                =

                        = 0 % (datar)

            g₂            =

                                =

                        = 16,50 % (-)menurun

            A         = [ g₁  ] – [ g₂ ]

                        = [ 0 % ] – [ -16,5 % ]

                        = 16,5 %

       Dengan kecepatan ( V ) = 60 km/jam dan A = 16,50 %, maka dari  lampiran grafik III (PPGJR) panjang lengkung vertikal diperoleh Lv_tabel = 225 m. Sehingga:

            X₁           =  ( ½ Lv ) / 3

                        = ( ½ 225 ) / 3

                        = 37,5  m

            X₂           = X₁  x 2

                                =  37,5 x 2

                        = 75 m

            X₃        = X₂ + X₁

                                = 75 + 37,5

                        = 112,5  m

            Y₁        =

                        =  

                        = 0,516m

            Y₂        =

                        =  

                        = 2,063 m

            Y₃        =

                        =  

                        = 4,641 m

Dari persamaan  dapat dihitung:

Penentuan Elevasi

Elevasi PLV     = Elevasi B - ( g₁ x X₃ )

                                = 888 - ( 0 % x 112,5 )

                        = 888 m

Elevasi D         = Elevasi B - ( (g₁ x X₂) – Y₁ )

                                = 888 - ( ( 0 % x  75) – 0,516 ))

                        = 887,484 m

Elevasi E          = Elevasi B - ( ( g₁ x  X₁) – Y₂ )

                                = 888 - ( (0 % x  37,5) – 2,063 )

                        = 885,938 m

Elevasi PPV     = Elevasi B – Y₃

                                = 888 – 4,641

                        = 883,359 m

Elevasi F          = Elevasi B – (( g₂ x  X₁ ) – Y₂ )

                                = 888 - ((16,5% x  37,5 ) – 2,063)

                        = 879,75 m

Elevasi G         = Elevasi B - ((g₂ x  X₂ ) – Y₂ )

                                = 888 – (( 16,5 % x  75 ) – 2,063 )

                        = 873,563 m

Elevasi PTV     = Elevasi B – ( g₂ ( ½ Lv ))

                                = 888 – (16,5 % ( ½ 225 ))

                        = 869,438 m

Penentuan Stasioning

Sta PLV           = Sta B – X₃

                        = 35 + 600 – 112,5

                        = 35 + 487,500 m

Sta D                = Sta PLV + X₁

                        = 35 + 487 + 37,500

                        = 35 + 525  m

Sta E                = Sta PLV + X₂

                        = 35 + 487 + 75

                        = 35 + 562,5 m

Sta PPV            = Sta PLV + X₃

                        = 35 + 487  + 112,5

                        = 35 + 600

                       

Sta F                = Sta PPV + X₁

                        = 35 + 600  + 37,5

                        = 35 + 637,5 m

Sta G                = Sta PPV + X₂

                        = 35 + 600 + 75

                        = 35 + 675 m

Sta PTV           = Sta PPV + X₃

                        = 35 + 600  + 112,5

                        = 35 +  712,5 m

 

Gambar 3.1 Vertikal Cembung PPV₁

3.6.2        Vertikal Cekung PPV₂

Dikeahui data-data sebagai berikut:

·         Elevasi Sta A ( 35 + 700 )      = 871,5 m

·         Elevasi Sta B ( 35 + 750  )     = 863,8 m

·         Elevasi Sta C ( 35 + 800 )      = 861,5 m

·         V Rencana                              = 60 km/jam

            d₁         = ± ( Sta B – Sta A )

                        = ± ( 35 + 750 – 35 + 700 )

                        = 50 m

            d₂         = ± ( Sta C – Sta B )                                                                                                     = ± ( 35 + 800 – 35 + 750 )

                        = 50 m

            g₁            =

                                =

                        = 15,40 % (-) menurun

            g₂            =

                                =

                        = 4,6 % (-)menurun

            A         = [ g₁  ] – [ g₂ ]

                        = [-15,40 % ] – [ - 4,6 % % ]

                        = 10,80 %

       Dengan kecepatan ( V ) = 60 km/jam dan A = 10,80 %, maka dari  lampiran grafik III (PPGJR) panjang lengkung vertikal diperoleh Lv_tabel = 110 m. Sehingga:

            X₁           =  ( ½ Lv ) / 3

                        = ( ½ 110 ) / 3

                        = 18,3 m

            X₂           = X₁ x 2

                                = 18,3 x 2

                        = 36,7 m

            X₃        = X₂ + X₁

                                = 36,7 + 18,3

                        = 55 m

            Y₁        =

                        =  

                        = 0,165 m

            Y₂        =

                        =  

                        = 0,66 m

            Y₃        =

                        =  

                        = 1,485 m

Dari persamaan  dapat dihitung:

Penentuan Elevasi

Elevasi PLV     = Elevasi B + ( g₁ x X₃ )

                                = 863,8 + ( 15,4 % x 55)

                        = 872,27 m

Elevasi D         = Elevasi B + (( g₁ x  X₂ )+ Y₁ )

                                = 863,8 + (( 15,4 % x  36,67) + 0,165 )

                        = 869,61 m

Elevasi E          = Elevasi B + (( g₁ x  X₁ )+ Y₂ )

                                = 863,8 + ( 15,4 % x (18,3  + 0,6))

                        = 867,28 m

Elevasi PPV     = Elevasi B + Y₃

                                = 863,8 + 1,485

                        = 865,26 m

Elevasi F          = Elevasi B + (( g₂ x  X₁ ) + Y₂ )

                                = 863,8 + (( 4,6 % x  18,33 ) + 1,833 )

                        = 865,303 m

Elevasi G         = Elevasi B + (( g₂ x  X₂ ) + Y₂ )

                                = 863,8 + (( 4,6 % x  36,67 ) + 0,66 )

                        = 866,147 m

Elevasi PTV     = Elevasi B + ( g₂ ( ½ Lv ))

                                = 863,8 + ( 4,6 % ( ½ 110 ))

                        = 886,33 m

Penentuan Stasioning

Sta PLV           = Sta B - X₃

                        = 35 + 750  - 55

                        = 35 + 695 m

Sta D                = Sta PLV + X₁

                        = 35 + 695 + 18,33

                        = 35 + 713,33 m

Sta E                = Sta PLV + X₂

                        = 35 + 695 + 36,67

                        = 35 +  731,67 m

Sta PPV            = Sta PLV + X₃

                        = 35 + 695 + 55  

                        = 35 + 750

                       

Sta F                = Sta PPV + X₁

                        = 35 + 750 + 18,33

                        = 35 + 768,33 m

Sta G                = Sta PPV + X₂

                        = 35 + 750 + 36,67

                        = 35 + 786,67 m

Sta PTV           = Sta PPV + X₃

                        = 35 + 750 + 55

                        = 35 + 805 m

 

Gambar 3.2 Vertikal Cekung PPV₂