Mathcad - Gr Long 20x40 C30_37

Dimensionare si armare grinda longitudinala 20x40 cm C30/37: •BETON C30/37 OTEL S500

fyk 500 103⋅

kN

m2:=fck 30 103

×kN

m2:=

γs 1.15:=

γc 1.5:=

fydfykγs

4.348 105×

kN

m2⋅=:=

fcdfckγc

2 104×

kN

m2⋅=:=

fctm 2.9 103⋅

kN

m2:=

Cnom 0.030m:=

ϕtrans 0.008m:=

ϕlong 0.025m:=

a Cnom ϕtrans+ϕlong

2+ 0.051 m=:=

hgL 0.4m:= rezulta d hgL a− 0.35m=:=

cota +4.55

Grinda marginala A-B ( ax 1)

MA.B.c 17.04kN m⋅:=

bgL 0.20m:=

μMA.B.c

fcd bgL⋅ d2⋅

0.035=:= μlim 0.372:= clasa beton C30/37 < C50/60

Conditie "Armare simpla" μ μlim<if

"Armare dubla" otherwise

:= Conditie "Armare simpla"=

ω 1 1 2 μ⋅−− 0.036=:=

Asnec ω bgL⋅ d⋅fcdfyd

⋅ 1.142 cm2⋅=:=

Asmax 0.04 bgL⋅ d⋅ 27.96 cm2⋅=:=Asmin 0.26

fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Conditie "INDEPLINITA" Asmin Asnec< Asmax<if

"NEINDEPLINITA" otherwise

:=Conditie "INDEPLINITA"=

As.c.l 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MA.B.st.neg.red 28.52kN m⋅:=

μMA.B.st.neg.red

fcd bgL⋅ d2⋅

0.058=:=



:=Conditie "Armare simpla"=

ω 1 1 2 μ⋅−− 0.06=:=


⋅ 1.935 cm2⋅=:=




AA.B.stg.neg 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.negAA.B.stg.neg fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.negxA.B.stg.neg

d0.088=:=

MRb.A.B.stg.neg λ η⋅ fcd⋅ ξA.B.stg.neg⋅ 1 0.50 λ⋅ ξA.B.stg.neg⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.neg.red 30.65kN m⋅:=

μMA.B.dr.neg.red

fcd bgL⋅ d2⋅

0.063=:=




ω 1 1 2 μ⋅−− 0.065=:=


⋅ 2.085 cm2⋅=:=




AA.B.dr.neg 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.negAA.B.dr.neg fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.negxA.B.dr.neg

d0.088=:=

MRb.A.B.dr.neg λ η⋅ fcd⋅ ξA.B.dr.neg⋅ 1 0.50 λ⋅ ξA.B.dr.neg⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.st.poz.red 12.85kN m⋅:=

μMA.B.st.poz.red

fcd bgL⋅ d2⋅

0.026=:=




ω 1 1 2 μ⋅−− 0.027=:=


⋅ 0.857 cm2⋅=:=



:=Conditie "NEINDEPLINITA"=

AA.B.st.poz 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C 30/37 < C50/60

xA.B.stg.pozAA.B.st.poz fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.pozxA.B.stg.poz

d0.088=:=

MRb.A.B.stg.poz λ η⋅ fcd⋅ ξA.B.stg.poz⋅ 1 0.50 λ⋅ ξA.B.stg.poz⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.poz.red 6.58kN m⋅:=

μMA.B.dr.poz.red

fcd bgL⋅ d2⋅

0.013=:=




ω 1 1 2 μ⋅−− 0.014=:=


⋅ 0.436 cm2⋅=:=



:=

Conditie "NEINDEPLINITA"=

AA.B.dr.poz 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C30/37

xA.B.dr.pozAA.B.dr.poz fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.pozxA.B.dr.poz

d0.088=:=

MRb.A.B.dr.poz λ η⋅ fcd⋅ ξA.B.dr.poz⋅ 1 0.50 λ⋅ ξA.B.dr.poz⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

Armare la forta taietoarelc 3.90m 0.35m− 3.55m=:=

Aafr 3.80m2:=

q 2.5kN

m2:= rezulta qr Aafr

q

lc⋅ 2.676

kNm

⋅=:=

pp 5.12kN

m2:= rezulta pr

pp Aafr⋅

lc5.481

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.A.B.dr.maxMRb.A.B.stg.neg MRb.A.B.dr.poz+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 43.734 kN⋅=:=

Ved.st.A.B.maxMRb.A.B.dr.neg MRb.A.B.stg.poz+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 43.734 kN⋅=:=

Vrd.A.B.st.calcstatic 34.16kN:=

Vrd.A.B.dr.calcstatic 37.47kN:=

Ved.A.B. max Ved.A.B.dr.max Ved.st.A.B.max, Vrd.A.B.st.calcstatic, Vrd.A.B.dr.calcstatic, ( ) 43.734 kN⋅=:=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=

bgL 0.2 m=rezulta ρs

As.c.lbgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.A.B. 43.734 kN⋅=

Ved.A.B. VRd.c> 1= este necesar calculul la forta taietoare

VRd.max.ctgθ2.5 0.13 bgL⋅ d⋅ fck⋅ 272.61 kN⋅=:=

Ved.A.B. VRd.max.ctgθ2.5< 1=

ctgθ 2.5:=

Asws

Ved.A.B.0.9 d⋅ fyd⋅ ctgθ⋅

0.128 mm⋅=:=Asw

s

Distanta maxima intre etrieri:•

sl.max 0.75 d⋅ 0.262 m=:=


Ved.A.B. VRd.max.ctgθ1.00< 1=

se adopta ctgθ 1.75:=

Asws

Ved.A.B.0.9 d⋅ fyd⋅ ctgθ⋅

0.183 mm⋅=:=Asw

s

Aleg

s 250mm:=

AswVed.A.B.

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.457 cm2

⋅=:=

AetrAsw

20.228 cm2

⋅=:=

REZULTA Aseffetr 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.sAseffetr

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 77.297 kN⋅=:=

VRd.s Ved.A.B.≥ 1=

Grinda marginala B -C (ax 1)

MB.C.c 22.51kN m⋅:=

bgL 0.20m:=

μMB.C.c

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.047=:=


⋅ 1.517 cm2⋅=:=

Asmin 0.26fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Asmax 0.04 bgL⋅ d⋅ 27.96 cm2⋅=:=




As.c.l 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MB.C.st.neg.red 30.17kN m⋅:=

μMB.C.st.neg.red

fcd bgL⋅ d2⋅

0.062=:=




ω 1 1 2 μ⋅−− 0.064=:=


⋅ 2.051 cm2⋅=:=



:=

Conditie "INDEPLINITA"=

AB.C.stg.neg 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.negAB.C.stg.neg fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.negxB.C.stg.neg

d0.088=:=

MRb.B.C.stg.neg λ η⋅ fcd⋅ ξB.C.stg.neg⋅ 1 0.50 λ⋅ ξB.C.stg.neg⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.dr.neg.red 32.10kN m⋅:=

μMB.C.dr.neg.red

fcd bgL⋅ d2⋅

0.066=:=




ω 1 1 2 μ⋅−− 0.068=:=


⋅ 2.187 cm2⋅=:=



:=


AB.C.dr.neg 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.negAB.C.dr.neg fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.negxB.C.dr.neg

d0.088=:=

MRb.B.C.dr.neg λ η⋅ fcd⋅ ξB.C.dr.neg⋅ 1 0.50 λ⋅ ξB.C.dr.neg⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.st.poz.red 0.34kN m⋅:=

μMB.C.st.poz.red

fcd bgL⋅ d2⋅

6.959 10 4−×=:=




ω 1 1 2 μ⋅−− 6.961 10 4−×=:=


⋅ 0.022 cm2⋅=:=



:=


AB.C.st.poz 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.pozAB.C.st.poz fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.pozxB.C.stg.poz

d0.088=:=

MRb.B.C.stg.poz λ η⋅ fcd⋅ ξB.C.stg.poz⋅ 1 0.50 λ⋅ ξB.C.stg.poz⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.dr.poz.red 0kN m⋅:=

μMB.C.dr.poz.red

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.dr.poz 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.pozAB.C.dr.poz fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.pozxB.C.dr.poz

d0.088=:=

MRb.B.C.dr.poz λ η⋅ fcd⋅ ξB.C.dr.poz⋅ 1 0.50 λ⋅ ξB.C.dr.poz⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr 5.29m2:=

q 2.5kN

m2:= rezulta qr Aafr

q

lc⋅ 3.112

kNm

⋅=:=

pp 5.12kN

m2:= rezulta pr

pp Aafr⋅

lc6.373

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.B.C.dr.maxMRb.B.C.stg.neg MRb.B.C.dr.poz+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 49.545 kN⋅=:=

Ved.st.B.C.maxMRb.B.C.dr.neg MRb.B.C.stg.poz+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 49.545 kN⋅=:=

Vrd.B.C.st.calcstatic 41.47kN:=

Vrd.B.C.dr.calcstatic 41.85kN:=

Ved.B.C max Ved.B.C.dr.max Ved.st.B.C.max, Vrd.B.C.st.calcstatic, Vrd.B.C.dr.calcstatic, ( ) 49.545 kN⋅=:=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=

bgL 0.2 m= REZULTA ρsAs.c.lbgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c. cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c VRd.c. N⋅ 25.657 kN⋅=:=

Ved.B.C 49.545 kN⋅=

Ved.B.C VRd.c> 1= este necesar calculul la forta taietoare


Ved.B.C VRd.max.ctgθ2.5< 1=

ctgθ 2.5:=

Asws

Ved.B.C0.9 d⋅ fyd⋅ ctgθ⋅

0.145 mm⋅=:=Asw

s


sl.max 0.75 d⋅ 0.262 m=:=


Ved.B.C VRd.max.ctgθ1.00< 1=


Asws


0.207 mm⋅=:=Asw

s

Aleg

s 250mm:=

AswVed.B.C

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.518 cm2

⋅=:=

AetrAsw

20.259 cm2

⋅=:=

Aseffetr 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.sAseffetr

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 77.297 kN⋅=:=

VRd.s Ved.B.C≥ 1=

Grinda centrala A-B ( ax 2)

MA.B.c2 25.53kN m⋅:=

bgL 0.20m:=

μMA.B.c2

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.054=:=

Asnec2 ω bgL⋅ d⋅fcdfyd

⋅ 1.726 cm2⋅=:=


fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Conditie "INDEPLINITA" Asmin Asnec2< Asmax<if



As.c.l2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MA.B.st.neg.red2 33.21kN m⋅:=

μMA.B.st.neg.red2

fcd bgL⋅ d2⋅

0.068=:=




ω 1 1 2 μ⋅−− 0.07=:=


⋅ 2.265 cm2⋅=:=




AA.B.stg.neg2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.neg2AA.B.stg.neg2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.neg2xA.B.stg.neg2

d0.088=:=

MRb.A.B.stg.neg2 λ η⋅ fcd⋅ ξA.B.stg.neg2⋅ 1 0.50 λ⋅ ξA.B.stg.neg2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.neg.red2 35.12kN m⋅:=

μMA.B.dr.neg.red2

fcd bgL⋅ d2⋅

0.072=:=




ω 1 1 2 μ⋅−− 0.075=:=


⋅ 2.401 cm2⋅=:=




AA.B.dr.neg2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.neg2AA.B.dr.neg2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.046 m=:=

ξA.B.dr.neg2xA.B.dr.neg2

d0.132=:=

MRb.A.B.dr.neg2 λ η⋅ fcd⋅ ξA.B.dr.neg2⋅ 1 0.50 λ⋅ ξA.B.dr.neg2⋅−( )⋅ bgL⋅ d2⋅ 48.837 kN m⋅⋅=:=

MA.B.st.poz.red2 3.68kN m⋅:=

μMA.B.st.poz.red2

fcd bgL⋅ d2⋅

7.532 10 3−×=:=




ω 1 1 2 μ⋅−− 7.56 10 3−×=:=


⋅ 0.243 cm2⋅=:=



:=Conditie "NEINDEPLINITA"=

AA.B.st.poz2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.poz2AA.B.st.poz2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.poz2xA.B.stg.poz2

d0.088=:=

MRb.A.B.stg.poz2 λ η⋅ fcd⋅ ξA.B.stg.poz2⋅ 1 0.50 λ⋅ ξA.B.stg.poz2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.poz.red2 10.66kN m⋅:=

μMA.B.dr.poz.red2

fcd bgL⋅ d2⋅

0.022=:=




ω 1 1 2 μ⋅−− 0.022=:=


⋅ 0.709 cm2⋅=:=



:=


AA.B.dr.poz2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/ < C50/60

xA.B.dr.poz2AA.B.dr.poz2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.poz2xA.B.dr.poz2

d0.088=:=

MRb.A.B.dr.poz2 λ η⋅ fcd⋅ ξA.B.dr.poz2⋅ 1 0.50 λ⋅ ξA.B.dr.poz2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr2 7.60m2:=

q 2.5kN

m2:= rezulta qr Aafr2

q

lc⋅ 5.352

kNm

⋅=:=

pp 5.12kN

m2:= rezulta pr

pp Aafr2⋅

lc10.961

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.A.B.dr.max2MRb.A.B.stg.neg2 MRb.A.B.dr.poz2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 63.991 kN⋅=:=

Ved.st.A.B.max2MRb.A.B.dr.neg2 MRb.A.B.stg.poz2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 68.407 kN⋅=:=

Vrd.A.B.st.calcstatic2 47.62kN:=

Vrd.A.B.dr.calcstatic2 50.77kN:=

Ved.A.B2. max Ved.A.B.dr.max2 Ved.st.A.B.max2, Vrd.A.B.st.calcstatic2, Vrd.A.B.dr.calcstatic2, ( ) 68.407 kN⋅=:=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=


As.c.l2bgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.A.B2. 68.407 kN⋅=

Ved.A.B2. VRd.c> 1= este necesar calculul la forta taietoare

VRd.max.ctgθ2.5.2 0.13 bgL⋅ d⋅ fck⋅ 272.61 kN⋅=:=

Ved.A.B2. VRd.max.ctgθ2.5< 1=

ctgθ 2.5:=

Asws

Ved.A.B2.0.9 d⋅ fyd⋅ ctgθ⋅

0.2 mm⋅=:=Asw

s


sl.max2 0.75 d⋅ 0.262 m=:=


Ved.A.B2. VRd.max.ctgθ1.00.2< 1=


Asws

Ved.A.B2.0.9 d⋅ fyd⋅ ctgθ⋅

0.286 mm⋅=:=Asw

s

Aleg

s 250mm:=

AswVed.A.B2.

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.715 cm2

⋅=:=

AetrAsw

20.357 cm2

⋅=:=

REZULTA Aseffetr2 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.sAseffetr

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 77.297 kN⋅=:=


Grinda centrala B -C (ax 2)

MB.C.c2 34.15kN m⋅:=

bgL 0.20m:=

μMB.C.c2

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.073=:=


⋅ 2.332 cm2⋅=:=

Asmin 0.26fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Asmax 0.04 bgL⋅ d⋅ 27.96 cm2⋅=:=




As.c.l2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

MB.C.st.neg.red2 39.71kN m⋅:=

μMB.C.st.neg.red2

fcd bgL⋅ d2⋅

0.081=:=




ω 1 1 2 μ⋅−− 0.085=:=


⋅ 2.729 cm2⋅=:=



:=


AB.C.stg.neg2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.neg2AB.C.stg.neg2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.046 m=:=

ξB.C.stg.neg2xB.C.stg.neg2

d0.132=:=

MRb.B.C.stg.neg2 λ η⋅ fcd⋅ ξB.C.stg.neg2⋅ 1 0.50 λ⋅ ξB.C.stg.neg2⋅−( )⋅ bgL⋅ d2⋅ 48.837 kN m⋅⋅=:=

MB.C.dr.neg.red2 43.28kN m⋅:=

μMB.C.dr.neg.red2

fcd bgL⋅ d2⋅

0.089=:=




ω 1 1 2 μ⋅−− 0.093=:=


⋅ 2.987 cm2⋅=:=



:=


AB.C.dr.neg2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.neg2AB.C.dr.neg2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.046 m=:=

ξB.C.dr.neg2xB.C.dr.neg2

d0.132=:=

MRb.B.C.dr.neg2 λ η⋅ fcd⋅ ξB.C.dr.neg2⋅ 1 0.50 λ⋅ ξB.C.dr.neg2⋅−( )⋅ bgL⋅ d2⋅ 48.837 kN m⋅⋅=:=

MB.C.st.poz.red2 0kN m⋅:=

μMB.C.st.poz.red2

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.st.poz2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.poz2AB.C.st.poz2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.poz2xB.C.stg.poz2

d0.088=:=

MRb.B.C.stg.poz2 λ η⋅ fcd⋅ ξB.C.stg.poz2⋅ 1 0.50 λ⋅ ξB.C.stg.poz2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.dr.poz.red2 0kN m⋅:=

μMB.C.dr.poz.red2

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.dr.poz2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.poz2AB.C.dr.poz2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.poz2xB.C.dr.poz2

d0.088=:=

MRb.B.C.dr.poz2 λ η⋅ fcd⋅ ξB.C.dr.poz2⋅ 1 0.50 λ⋅ ξB.C.dr.poz2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr2 10.58m2:=

q 2.5kN

m2:= rezulta qr Aafr2

q

lc⋅ 6.224

kNm

⋅=:=

pp 5.47kN

m2:= rezulta pr

pp Aafr2⋅

lc13.617

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.B.C.dr.max2MRb.B.C.stg.neg2 MRb.B.C.dr.poz2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 83.933 kN⋅=:=

Ved.st.B.C.max2MRb.B.C.dr.neg2 MRb.B.C.stg.poz2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 83.933 kN⋅=:=

Vrd.B.C.st.calcstatic2 58.15kN:=

Vrd.B.C.dr.calcstatic2 58.61kN:=

Ved.B.C2 max Ved.B.C.dr.max2 Ved.st.B.C.max2, Vrd.B.C.st.calcstatic2, Vrd.B.C.dr.calcstatic2, ( ) 83.933 kN⋅=:=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=

bgL 0.2 m= REZULTA ρsAs.c.l2bgL d⋅

4.854 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.937 104

×=:=

VRd.c 29.37kN:=

Ved.B.C2 83.933 kN⋅=

Ved.B.C VRd.c> 1= este necesar calculul la forta taietoare


Ved.B.C2 VRd.max.ctgθ2.5.2< 1=

ctgθ 2.5:=

Asws


0.245 mm⋅=:=Asw

s


sl.max 0.75 d⋅ 0.262 m=:=


Ved.B.C2 VRd.max.ctgθ1.00.2< 1=


Asws


0.351 mm⋅=:=Asw

s

Aleg

s 200mm:=

AswVed.B.C2

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.701 cm2

⋅=:=

Aetr2Asw

20.351 cm2

⋅=:=

Aseffetr2 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.s2Aseffetr2

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 96.622 kN⋅=:=

VRd.s2 Ved.B.C2≥ 1=

cota +8.45

Grinda marginala A-B ( ax 1)

MA.B.c.z1 16.41kN m⋅:=

bgL 0.20m:=

μMA.B.c.z1

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.034=:=

Asnec.z1 ω bgL⋅ d⋅fcdfyd

⋅ 1.099 cm2⋅=:=


fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Conditie "INDEPLINITA" Asmin Asnec.z1< Asmax<if



As.c.l.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MA.B.st.neg.red.z1 11.18kN m⋅:=

μMA.B.st.neg.red.z1

fcd bgL⋅ d2⋅

0.023=:=




ω 1 1 2 μ⋅−− 0.023=:=


⋅ 0.744 cm2⋅=:=



:=


AA.B.stg.neg.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.neg.z1AA.B.stg.neg.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.neg.z1xA.B.stg.neg.z1

d0.088=:=

MRb.A.B.stg.neg.z1 λ η⋅ fcd⋅ ξA.B.stg.neg.z1⋅ 1 0.50 λ⋅ ξA.B.stg.neg.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.neg.red.z1 24.27kN m⋅:=

μMA.B.dr.neg.red.z1

fcd bgL⋅ d2⋅

0.05=:=




ω 1 1 2 μ⋅−− 0.051=:=


⋅ 1.639 cm2⋅=:=




AA.B.dr.neg.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.neg.z1AA.B.dr.neg.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.neg.z1xA.B.dr.neg.z1

d0.088=:=

MRb.A.B.dr.neg.z1 λ η⋅ fcd⋅ ξA.B.dr.neg.z1⋅ 1 0.50 λ⋅ ξA.B.dr.neg.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.st.poz.red.z1 9.58kN m⋅:=

μMA.B.st.poz.red.z1

fcd bgL⋅ d2⋅

0.02=:=




ω 1 1 2 μ⋅−− 0.02=:=


⋅ 0.637 cm2⋅=:=



:=


AA.B.st.poz.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.poz.z1AA.B.st.poz.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.poz.z1xA.B.stg.poz.z1

d0.088=:=

MRb.A.B.stg.poz.z1 λ η⋅ fcd⋅ ξA.B.stg.poz.z1⋅ 1 0.50 λ⋅ ξA.B.stg.poz.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.poz.red.z1 0kN m⋅:=

μMA.B.dr.poz.red.z1

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AA.B.dr.poz.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.poz.z1AA.B.dr.poz.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.poz.z1xA.B.dr.poz.z1

d0.088=:=

MRb.A.B.dr.poz.z1 λ η⋅ fcd⋅ ξA.B.dr.poz.z1⋅ 1 0.50 λ⋅ ξA.B.dr.poz.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr.z1 3.80m2:=

q 1kN

m2:= rezulta qr Aafr.z1

q

lc⋅ 1.07

kNm

⋅=:=

pp 12.54kN

m2:= rezulta pr

pp Aafr.z1⋅

lc13.423

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.A.B.dr.max.z1MRb.A.B.stg.neg.z1 MRb.A.B.dr.poz.z1+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 58.491 kN⋅=:=

Ved.st.A.B.max.z1MRb.A.B.dr.neg.z1 MRb.A.B.stg.poz.z1+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 58.491 kN⋅=:=

Vrd.A.B.st.calcstatic.z1 21.81kN:=

Vrd.A.B.dr.calcstatic.z1 30.91kN:=

Ved.A.B.z1 max Ved.A.B.dr.max.z1 Ved.st.A.B.max.z1, Vrd.A.B.st.calcstatic.z1, Vrd.A.B.dr.calcstatic.z1, ( ):=

Ved.A.B.z1 58.491 kN⋅=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=


As.c.l.z1bgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.A.B.z1 58.491 kN⋅=

Ved.A.B. VRd.c> 1= este necesar calculul la forta taietoare

VRd.max.ctgθ2.5.z1 0.13 bgL⋅ d⋅ fck⋅ 272.61 kN⋅=:=

Ved.A.B.z1 VRd.max.ctgθ2.5.z1< 1=

ctgθ 2.5:=

Asws

Ved.A.B.z10.9 d⋅ fyd⋅ ctgθ⋅

0.171 mm⋅=:=Asw

s


sl.max.z1 0.75 d⋅ 0.262 m=:=




Asws


0.244 mm⋅=:=Asw

s

Aleg

s 250mm:=

AswVed.A.B.z1

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.611 cm2

⋅=:=

Aetr.z1Asw

20.305 cm2

⋅=:=

REZULTA Aseffetr.z1 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.s.z1Aseffetr.z1

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 77.297 kN⋅=:=


Grinda marginala B -C (ax 1)

MB.C.c.z1 18.28kN m⋅:=

bgL 0.20m:=

μMB.C.c.z1

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.038=:=


⋅ 1.226 cm2⋅=:=

Asmin 0.26fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Asmax 0.04 bgL⋅ d⋅ 27.96 cm2⋅=:=




As.c.l.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MB.C.st.neg.red.z1 21.88kN m⋅:=

μMB.C.st.neg.red.z1

fcd bgL⋅ d2⋅

0.045=:=




ω 1 1 2 μ⋅−− 0.046=:=


⋅ 1.474 cm2⋅=:=



:=


AB.C.stg.neg.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.neg.z1AB.C.stg.neg.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.neg.z1xB.C.stg.neg.z1

d0.088=:=

MRb.B.C.stg.neg.z1 λ η⋅ fcd⋅ ξB.C.stg.neg.z1⋅ 1 0.50 λ⋅ ξB.C.stg.neg.z1⋅−( )⋅ bgL⋅ d2⋅ kN m⋅⋅=:=

MB.C.dr.neg.red.z1 23.48kN m⋅:=

μMB.C.dr.neg.red.z1

fcd bgL⋅ d2⋅

0.048=:=




ω 1 1 2 μ⋅−− 0.049=:=


⋅ 1.584 cm2⋅=:=



:=


AB.C.dr.neg.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.neg.z1AB.C.dr.neg.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.neg.z1xB.C.dr.neg.z1

d0.088=:=

MRb.B.C.dr.neg.z1 λ η⋅ fcd⋅ ξB.C.dr.neg.z1⋅ 1 0.50 λ⋅ ξB.C.dr.neg.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.st.poz.red.z1 0kN m⋅:=

μMB.C.st.poz.red.z1

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.st.poz.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.poz.z1AB.C.st.poz.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.poz.z1xB.C.stg.poz.z1

d0.088=:=

MRb.B.C.stg.poz.z1 λ η⋅ fcd⋅ ξB.C.stg.poz.z1⋅ 1 0.50 λ⋅ ξB.C.stg.poz.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.dr.poz.red.z1 0kN m⋅:=

μMB.C.dr.poz.red.z1

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.dr.poz.z1 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.poz.z1AB.C.dr.poz.z1 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.poz.z1xB.C.dr.poz.z1

d0.088=:=

MRb.B.C.dr.poz.z1 λ η⋅ fcd⋅ ξB.C.dr.poz.z1⋅ 1 0.50 λ⋅ ξB.C.dr.poz.z1⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr.z1 5.29m2:=

q 1kN


q

lc⋅ 1.245

kNm

⋅=:=

pp 13.22kN

m2:= rezulta pr

pp Aafr.z1⋅

lc16.455

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.B.C.dr.max.z1MRb.B.C.stg.neg.z1 MRb.B.C.dr.poz.z1+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 72.516 kN⋅=:=

Ved.st.B.C.max.z1MRb.B.C.dr.neg.z1 MRb.B.C.stg.poz.z1+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 72.516 kN⋅=:=

Vrd.B.C.st.calcstatic.z1 30.86kN:=

Vrd.B.C.dr.calcstatic.z1 31.31kN:=

Ved.B.C.z1 max Ved.B.C.dr.max.z1 Ved.st.B.C.max.z1, Vrd.B.C.st.calcstatic.z1, Vrd.B.C.dr.calcstatic.z1, ( ):=

Ved.B.C.z1 72.516 kN⋅=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=

bgL 0.20m:=REZULTA ρs

As.c.l.z1bgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.B.C.z1 72.516 kN⋅=

Ved.B.C.z1 VRd.c> 1= este necesar calculul la forta taietoare


Ved.B.C.z1 VRd.max.ctgθ2.5.z1< 1=

ctgθ 2.5:=

Asws

Ved.B.C.z10.9 d⋅ fyd⋅ ctgθ⋅

0.212 mm⋅=:=Asw

s


sl.max 0.75 d⋅ 0.262 m=:=




Asws


0.303 mm⋅=:=Asw

s

Aleg

s 250mm:=

AswVed.B.C.z1

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.757 cm2

⋅=:=

Aetr.z1Asw

20.379 cm2

⋅=:=

Aseffetr.z1 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.s.z1Aseffetr.z1

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 77.297 kN⋅=:=

VRd.s.z1 Ved.B.C.z1≥ 1=

Grinda centrala A-B ( ax 2)

MA.B.c.z2 24.42kN m⋅:=

bgL 0.20m:=

μMA.B.c.z2

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.051=:=


⋅ 1.649 cm2⋅=:=


fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=




As.c.l.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MA.B.st.neg.red.z2 15.98kN m⋅:=

μMA.B.st.neg.red.z2

fcd bgL⋅ d2⋅

0.033=:=




ω 1 1 2 μ⋅−− 0.033=:=


⋅ 1.069 cm2⋅=:=



:=


AA.B.stg.neg.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.neg.z2AA.B.stg.neg.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.neg.z2xA.B.stg.neg.z2

d0.088=:=

MRb.A.B.stg.neg.z2 λ η⋅ fcd⋅ ξA.B.stg.neg.z2⋅ 1 0.50 λ⋅ ξA.B.stg.neg.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.neg.red.z2 30.93kN m⋅:=

μMA.B.dr.neg.red.z2

fcd bgL⋅ d2⋅

0.063=:=




ω 1 1 2 μ⋅−− 0.065=:=


⋅ 2.104 cm2⋅=:=




AA.B.dr.neg.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.neg.z2AA.B.dr.neg.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.neg.z2xA.B.dr.neg.z2

d0.088=:=

MRb.A.B.dr.neg.z2 λ η⋅ fcd⋅ ξA.B.dr.neg.z2⋅ 1 0.50 λ⋅ ξA.B.dr.neg.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.st.poz.red.z2 1.04kN m⋅:=

μMA.B.st.poz.red.z2

fcd bgL⋅ d2⋅

2.129 10 3−×=:=




ω 1 1 2 μ⋅−− 2.131 10 3−×=:=


⋅ 0.069 cm2⋅=:=



:=


AA.B.st.poz.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.stg.poz.z2AA.B.st.poz.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.stg.poz.z2xA.B.stg.poz.z2

d0.088=:=

MRb.A.B.stg.poz.z2 λ η⋅ fcd⋅ ξA.B.stg.poz.z2⋅ 1 0.50 λ⋅ ξA.B.stg.poz.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MA.B.dr.poz.red.z2 0kN m⋅:=

μMA.B.dr.poz.red.z2

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AA.B.dr.poz.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xA.B.dr.poz.z2AA.B.dr.poz.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξA.B.dr.poz.z2xA.B.dr.poz.z2

d0.088=:=

MRb.A.B.dr.poz.z2 λ η⋅ fcd⋅ ξA.B.dr.poz.z2⋅ 1 0.50 λ⋅ ξA.B.dr.poz.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr.z2 7.60m2:=

q 1kN


q

lc⋅ 2.141

kNm

⋅=:=

pp 13.22kN

m2:= rezulta pr

pp Aafr.z2⋅

lc28.302

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.A.B.dr.max.z2MRb.A.B.stg.neg.z2 MRb.A.B.dr.poz.z2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 96.994 kN⋅=:=

Ved.st.A.B.max.z2MRb.A.B.dr.neg.z2 MRb.A.B.stg.poz.z2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 96.994 kN⋅=:=

Vrd.A.B.st.calcstatic.z2 42.02kN:=

Vrd.A.B.dr.calcstatic.z2 49.86kN:=

Ved.A.B.z2 max Ved.A.B.dr.max.z2 Ved.st.A.B.max.z2, Vrd.A.B.st.calcstatic.z2, Vrd.A.B.dr.calcstatic.z2, ( ):=

Ved.A.B.z2 96.994 kN⋅=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=


As.c.l.z2bgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.A.B.z2 96.994 kN⋅=

Ved.A.B.z2 VRd.c> 1= este necesar calculul la forta taietoare



ctgθ 2.5:=

Asws


0.284 mm⋅=:=Asw

s


sl.max2 0.75 d⋅ 0.262 m=:=




Asws


0.405 mm⋅=:=Asw

s

Aleg

s 150mm:=

AswVed.A.B.z2

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.608 cm2

⋅=:=

Aetr.z2Asw

20.304 cm2

⋅=:=

REZULTA Aseffetr.z2 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.s.z2Aseffetr.z2

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 128.829 kN⋅=:=

VRd.s.z2 Ved.A.B.z2≥ 1=

Grinda centrala B -C (ax 2)

MB.C.c.z2 30.17kN m⋅:=

bgL 0.20m:=

μMB.C.c.z2

fcd bgL⋅ d2⋅





ω 1 1 2 μ⋅−− 0.064=:=


⋅ 2.051 cm2⋅=:=

Asmin 0.26fctmfyk

⋅ bgL⋅ d⋅ 1.054 cm2⋅=:=

Asmax 0.04 bgL⋅ d⋅ 27.96 cm2⋅=:=



:=


As.c.l.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

MB.C.st.neg.red.z2 36.94kN m⋅:=

μMB.C.st.neg.red.z2

fcd bgL⋅ d2⋅

0.076=:=




ω 1 1 2 μ⋅−− 0.079=:=


⋅ 2.531 cm2⋅=:=



:=


AB.C.stg.neg.z2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.neg.z2AB.C.stg.neg.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.046 m=:=

ξB.C.stg.neg.z2xB.C.stg.neg.z2

d0.132=:=

MRb.B.C.stg.neg.z2 λ η⋅ fcd⋅ ξB.C.stg.neg.z2⋅ 1 0.50 λ⋅ ξB.C.stg.neg.z2⋅−( )⋅ bgL⋅ d2⋅ 48.837 kN m⋅⋅=:=

MB.C.dr.neg.red.z2 39.76kN m⋅:=

μMB.C.dr.neg.red.z2

fcd bgL⋅ d2⋅

0.081=:=




ω 1 1 2 μ⋅−− 0.085=:=


⋅ 2.733 cm2⋅=:=



:=


AB.C.dr.neg.z2 3 π⋅12mm( )2

4⋅ 3.393 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.neg.z2AB.C.dr.neg.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.046 m=:=

ξB.C.dr.neg.z2xB.C.dr.neg.z2

d0.132=:=

MRb.B.C.dr.neg.z2 λ η⋅ fcd⋅ ξB.C.dr.neg.z2⋅ 1 0.50 λ⋅ ξB.C.dr.neg.z2⋅−( )⋅ bgL⋅ d2⋅ 48.837 kN m⋅⋅=:=

MB.C.st.poz.red.z2 0kN m⋅:=

μMB.C.st.poz.red.z2

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.st.poz.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.stg.poz.z2AB.C.st.poz.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.stg.poz.z2xB.C.stg.poz.z2

d0.088=:=

MRb.B.C.stg.poz.z2 λ η⋅ fcd⋅ ξB.C.stg.poz.z2⋅ 1 0.50 λ⋅ ξB.C.stg.poz.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=

MB.C.dr.poz.red.z2 0kN m⋅:=

μMB.C.dr.poz.red.z2

fcd bgL⋅ d2⋅

0=:=




ω 1 1 2 μ⋅−− 0=:=


⋅ 0 cm2⋅=:=



:=


AB.C.dr.poz.z2 2 π⋅12mm( )2

4⋅ 2.262 cm2

⋅=:=

λ 0.8:= η 1:= clasa beton C30/37 < C50/60

xB.C.dr.poz.z2AB.C.dr.poz.z2 fyd⋅

bgL λ⋅ η⋅ fcd⋅0.031 m=:=

ξB.C.dr.poz.z2xB.C.dr.poz.z2

d0.088=:=

MRb.B.C.dr.poz.z2 λ η⋅ fcd⋅ ξB.C.dr.poz.z2⋅ 1 0.50 λ⋅ ξB.C.dr.poz.z2⋅−( )⋅ bgL⋅ d2⋅ 33.163 kN m⋅⋅=:=


Aafr.z2 10.58m2:=

q 1kN


q

lc⋅ 2.489

kNm

⋅=:=

pp 13.22kN

m2:= rezulta pr

pp Aafr.z2⋅

lc32.91

kNm

⋅=:=

pgL 0.20m 0.4⋅ m 25⋅kN

m32

kNm

⋅=:=

Ved.B.C.dr.max.z2MRb.B.C.stg.neg.z2 MRb.B.C.dr.poz.z2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 127.377 kN⋅=:=

Ved.st.B.C.max.z2MRb.B.C.dr.neg.z2 MRb.B.C.stg.poz.z2+

lc

pr 1.35⋅ pgL 1.35⋅+ 1.5 qr⋅+( ) lc⋅

2+ 127.377 kN⋅=:=

Vrd.B.C.st.calcstatic.z2 53.99kN:=

Vrd.B.C.dr.calcstatic.z2 54.95kN:=

Ved.B.C.z2 max Ved.B.C.dr.max.z2 Ved.st.B.C.max.z2, Vrd.B.C.st.calcstatic.z2, Vrd.B.C.dr.calcstatic.z2, ( ):=

Ved.B.C.z2 127.377 kN⋅=

cRd.c0.18γc

0.12=:= k 1200mm

d⎛⎜⎝

⎞⎟⎠

32

+ 1.433=:=

bgL 0.2 m= REZULTA ρsAs.c.l.z2bgL d⋅

3.236 10 3−×=:=

d 0.35m=

VRd.c cRd.c k⋅ 100 ρs⋅ fck⋅( )0.333⋅⎡

⎣⎤⎦ bgL⋅ d⋅:=

VRd.c cRd.c k⋅ 100 ρs⋅ 30⋅( )0.333⋅⎡

⎣⎤⎦ 200⋅ 350⋅ 2.566 104

×=:=

VRd.c 25.66kN:=

Ved.B.C.z2 127.377 kN⋅=

Ved.B.C.z2 VRd.c> 1= este necesar calculul la forta taietoare



ctgθ 2.5:=

Asws


0.373 mm⋅=:=Asw

s


sl.max 0.75 d⋅ 0.262 m=:=




Asws


0.532 mm⋅=:=Asw

s

Aleg

s 150mm:=

AswVed.B.C.z2

0.9 d⋅ fyd⋅ ctgθ⋅s⋅ 0.798 cm2

⋅=:=

Aetr.z2Asw

20.399 cm2

⋅=:=

Aseffetr.z2 23.14 6mm( )2⋅

4⋅ 0.565 cm2

⋅=:=

z 0.9 d⋅ 0.315 m=:=

α 90 °⋅:=

fywd fyd 434.783N

mm2⋅=:=

1tan α( ) 0=

VRd.s.z2Aseffetr.z2

sz⋅ fywd⋅ 2.5

1tan α( )+

⎛⎜⎝

⎞⎟⎠

⋅ sin α( )⋅ 128.829 kN⋅=:=

VRd.s.z2 Ved.B.C.z2≥ 1=

Mathcad - Gr Long 20x40 C30_37

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Transcript of Mathcad - Gr Long 20x40 C30_37