T028 (c) ibhxws webservices

Tragwerke, Schnittgroessen, Vorbemessung

Elastisch eingespannter Rahmen nach KLEINLOGEL

Rahmenform 28

Prinzipieller Ablauf der Nutzung des Dienstes:

1. Parameter eingeben bzw. waehlen

2. Dienst starten mit 'go' oder

2. Beispiel in Liste anklicken

3. Parameter aendern (weitere Nachweise)

4. Dienst starten mit 'go'

5. Ergebnistext markieren und kopieren

6. Ergebnistext in Ihre Dateien einfuegen

7. Mit ONLINE-PDF drucken oder lokal speichern

Structures, internal forces, predimensioning

Elastic end-restraint frame according to KLEINLOGEL

Frame shape 28

Using Webservice

1. Input or choose values

2. Start webservice with 'go' or

2. Start example in black list

3. Change values (new calculation, new action)

4. Start webservice once more with 'go'

5. Copy result sets of service to your local editors or programs or

6. Use ONLINE-PDF for printing or local saving

Hintergrundinformationen zum Webdienstes:

Background informations webservice:

Rahmenform 28 - frame shape 28
Festwerte - fixed values
k = (J2/J1)*(h/l)
N1 = (2 - epsilon)*k + 3
N2 = k + epsilon*(4*k + 1)
epsilon = Momentenfortleitungszahl
epsilon = 0 = freie Drehbarkeit, Gelenk (Rahmenform 29)
epsilon = 0.5 = volle Einspannung (Rahmenform 30)

Fall 28/1 - case 28/1
Gleichmäßige Wärmezunahme im ganzen Rahmen
T = 3*E*J2*alphat*t/(h*N1)
MA = MD = 3*epsilon*T*(k+1)/k
MB = MC = - (1+ epsilon)*T
My = MA - HA*y
HA = HD = T*(N2+ 2*epsilon)/(h*k)

Fall 28/2 - case 28/2
Rechteck-Vollast auf dem Riegel, symm
MA = MD = (epsilon*q*l^2)/(4*N1) = -epsilon*MB
MB = MC = - (q*l^2)/(4*N1)
maxM = (q*l^2)/8 + MB
VA = VD = q*l/2
HA = HD = - MB*(1 + epsilon)/h
Mx = q*x*x'/2 + MB
My = MA - HA*y
he = h*epsilon/(1 + epsilon)

Fall 28/3 - case 28/3
Rechteck-Streckenlast von links her auf dem Riegel
beta = b/l
MA = (q*epsilon*a^2)*[(1+2*beta)/N1 - (beta^2)/N2]/4
MD = (q*epsilon*a^2)*[(1+2*beta)/N1 + (beta^2)/N2]/4
MB = - (q*a^2)*[(1+2*beta)/N1 + epsilon*(beta^2)/N2]/4
MC = - (q*a^2)*[(1+2*beta)/N1 - epsilon*(beta^2)/N2]/4
VD = (q*a^2)*[1 - epsilon*(beta^2)/N2]/(2*l)
HA = HD = (q*a^2)*(1 + epsilon)*(1 + 2*beta)/(4*h*N1)
VA = q*a - VD
E*J1*uB = (q*h^2)*(1 + epsilon)*(a^2)*(beta^2)/(24*N2)
Mx = (VA - q*x/2)*x + MB Bereich a
Mx = VD*x' + MC Bereich b
My1 = MA - HA*y1
My2 = MD - HD*y2

Fall 28/4 - case 28/4
Einzellast an beliebiger Stelle des Riegels
alpha = a/l
beta = b/l
alpha + beta = 1
MA = P*a*b*[3*epsilon/(2*N1) - (beta - alpha)*epsilon/(2*N2)]/l
MD = P*a*b*[3*epsilon/(2*N1) + (beta - alpha)*epsilon/(2*N2)]/l
MB = - P*a*b*[3/(2*N1) + (beta - alpha)*epsilon/(2*N2)]/l
MC = - P*a*b*[3/(2*N1) - (beta - alpha)*epsilon/(2*N2)]/l
VA = P*beta*(1 + alpha*(beta - alpha)*epsilon/N2
HA = HD = 3*P*a*b*(1 + epsilon)/(2*l*h*N1)
VD = P - VA
MP = P*a*b/l + beta*MB + alpha*MC
My1 = MA - HA*y1
My2 = MD - HD*y2
Mx = Va*x + MB Bereich a area a
Mx = VD*x' + MC Bereich b area b
E*J1*uB = (P*l*h^2)*(1 + epsilon)*alpha*beta*(beta - alpha)/(12*N2)

Fall 28/5 - case 28/5
Zwei gleiche Einzellasten symmetrisch auf dem Riegel
alpha = a/l
MA = MD = -epsilon*MB
MB = MC = - 3*P*a*(1 - alpha)/N1
VA = VD = P
HA = HD = - MB*(1 + epsilon)/h
Mx = P*x + MB
My = MA - HA*y
he = h*epsilon/(1 + epsilon)

Fall 28/6 - case 28/6
Einzellast in der Mitte des Riegels
MA = MD = 3*P*l*epsilon/(8*N1) = -epsilon*MB
MB = MC = - 3*P*l/(8*N1)
VA = VD = P/2
HA = HD = - MB*(1 + epsilon)/h
MP = P*l/4 + MB
Mx = P*x/2 + MB
My = MA - HA*y
he = h*epsilon/(1 + epsilon)

Fall 28/7 - case 28/7
Drei gleiche Einzellasten in den Viertelpunkten des Riegels
MA = MD = 15*P*l*epsilon/(16*N1) = -epsilon*MB
MB = MC = - 15*P*l/(16*N1)
M1 = 3*P*l/8 + MB
M2 = P*l/2 + MB
HA = HD = - MB*(1 + epsilon)/h
VA = VD = 3*P/2
Mx = VA*x + MB
My = MA - Ha*y
he = h*epsilon/(1 + epsilon)

Fall 28/8 - case 28/8
Riegel beliebig senkrecht belastet
X1 = (L + R)/(2*N1)
X3 = (L - R)*epsilon/(2*N2)
MA = epsilon*X1 - X3
MD = epsilon*X1 + X3
MB = -X1 - X3
MC = -X1 + X3
VA = (Sr + 2*X3)/l
VD = F - VA
HA = HD = X1*(1 + epsilon)/h
My1 = MA - HA*y1
Mx = Mx0 + MB*x'/l + MC*x/l
My2 = MD - HD*y2
E*J1*uB = (h^2)*(1 + epsilon)*(L - R)/(12*N2)
==> Belastungsglieder - load terms: L, R, Sl, Sr, F, W, Mx0, My0

Fall 28/9 - case 28/9
Riegel beliebig senkrecht belastet, symm
MA = MD = L*epsilon/N1
HA = HD = - MB*(1 + epsilon)/h
VA = VD = F/2
MB = MC = - L/N1
Mx = Mx0 + MB
My = MA - HA*y
==> Belastungsglieder - load terms: L, R, Sl, Sr, F, W, Mx0, My0
he = h*epsilon/(1 + epsilon)

Fall 28/10 - case 28/10
Beide Stiele gleich belastet, von aussen her, symm
MA = MD = - (L*(2*k + 3) - R*k)*epsilon/N1
MB = MC = - (R - epsilon*L)*k/N1
HA = HD = - (Sr - MA + MB)/h
My = My0 + MA*y'/h + MB*y/h
==> Belastungsglieder - load terms: L, R, Sl, Sr, F, W, Mx0, My0

Fall 28/11 - case 28/11
Beide Stiele gleich belastet, von links her, asymm
MB = -MC = (Sl*(1 + epsilon) - epsilon*(L + R))*k/N2
MD = -MA = Sl - MB
HD = - HA = W
VD = -VA = 2*MB/l
Mx = (x' - x)*MB/l
My = My0 + MA*y'/h + MB*y/h
E*J1*uB = (h^2)*[Sl*(N1 - 2) - epsilon*L*(3*k + 1) + (1 + epsilon)*R*k]/(6*N2)
==> Belastungsglieder - load terms: L, R, Sl, Sr, F, W, Mx0, My0

Fall 28/12 - case 28/12
Linker Stiel beliebig waagerecht belastet
X1 = (L*(2*k + 3) - R*k)*epsilon/(2*N1)
X2 = (R - epsilon*L)*k/(2*N1)
X3 = ((1 + epsilon)*Sl - epsilon*(L + R))*k/(2*N2)
MA = - X1 - (0.5*Sl - X3)
MD = - X1 + (0.5*Sl - X3)
MB = -X2 + X3
MC = -X2 - X3
HD = Sl/(2*h) - (X1 - X2)/h
HA = - (W - HD)
VD = - VA = 2*X3/l
My1 = My0 + MA*y1'/h + MB*y1/h
Mx = MC + VD*x'
My2 = MD - HD*y2
E*J1*uB = (h^2)*[Sl*(N1 - 2) - epsilon*L*(3*k + 1) + (1 + epsilon)*R*k]/(12*N2)
==> Belastungsglieder - load terms: L, R, Sl, Sr, F, W, Mx0, My0

Fall 28/13 - case 28/13
Waagerechte Einzellast in Riegelhöhe
MA = - P*h*epsilon*(3*k + 1)/(2*N2)
MD = + P*h*epsilon*(3*k + 1)/(2*N2)
MB = P*h*(1 + epsilon)*k/(2*N2)
MC = - P*h*(1 + epsilon)*k/(2*N2)
HD = -HA = P/2
VD = - VA = 2*MB/l
My1 = MA + P*y1/2
Mx = (x' - x)*MB/l
My2 = MD - P*y2/2
E*J1*uB = (P*h^3)*(N1 - 2)/(12*N1)

Fall 28/14 - case 28/14
Einzellast an beliebiger Stelle des linken Riegels
alpha = a/h
beta = b/h
alpha + beta = 1
X1 = 3*P*a*b*(1+ beta + beta*k)*epsilon/(2*h*N1)
X2 = P*a*b*(1 + alpha - epsilon*(1 + beta)*k/(2*h*N1)
X3 = P*a*(1+ epsilon - 3*epsilon*beta)*k/(2*N2)
MA = - X1 - (0.5*P*a - X3)
MD = - X1 + (0.5*P*a - X3)
MB = -X2 + X3
MD = -X2 - X3
HD = (P*a)/(2*h) - (X1 - X2)/h
HA = -(P - HD)
VA = -VD = - 2*X3/l
MP = P*a*b/h + beta*MA + alpha*MB
Mx = MC + VD*x'
My2 = MD - HD*y2
My1 = MA - HA*y1 Bereich a area a
My1 = MB + HD*y1' Bereich b area b
E*J1*uB = (h^2)*[X1 + X2*(2*k + 3)/k + X3*(3*k +1)/k - P*a/2]/6

Fall 28/15 - case 28/15
Rechteck-Vollast am linken Stiel
MA = q*(h^2)*epsilon*[-(k +3)/(2*N1) - (4*k + 1)/N2]/4
MD = q*(h^2)*epsilon*[-(k +3)/(2*N1) + (4*k + 1)/N2]/4
MB = q*(h^2)*k*[-(1 - epsilon)/(2*N1) + 1/N2]/4
MC = q*(h^2)*k*[-(1 - epsilon)/(2*N1) - 1/N2]/4
HD = q*h*(5*k + 6 - epsilon*(4*k +3))/(8*N1)
HA = - (q*h - HD)
VD = -VA = q*(h^2)*k/(2*l*N2)
My1 = 0.5*q*y1*y1' + MA*y1'/h + MB*y1/h
Mx = MC + VD*x'
My2 = MD - HD*y2
E*J1*uB = (q*h^4)*(6*k + 2 -N2)/(48*N2)

Fall 28/16 - case 28/16
Rechteck-Vollast an beiden Stielen, symm
MA = MD = - q*(h^2)*epsilon*(k + 3)/(4*N1)
MB = MC = - q*(h^2)*k*(1 - epsilon)/(4*N1)
HA = HD = - 3*q*h*(k + 2 +epsilon)/(4*N1)
My = 0.5*q*y*y' + MA*y'/h + MB*y/h

Fall 28/17 - case 28/17
Dreiecklast an beiden Stielen, symm
MA = MD = - p*(h^2)*epsilon*(3*k + 8)/(20*N1)
MB = MC = - p*(h^2)*k*(7 - 8*epsilon)/(60*N1)
HA = HD = - p*h*(11*k + 20 + epsilon*(8 - k)/(20*N1)
My = p*(h^2)*omegaD'/6 + MA*y'/h + MB*y/h
omegaD' = y'/h - (y'/h)^3

Fall 28/18 - case 28/18
Momente an den Ecken, symm
MA = MD = - 3*epsilon*M/N1
MB1 = MC1 = 3*M/N1
MB2 = MC2 = - M*k*(2 - epsilon)/N1
MB1 - MB2 = M
HA = HD = - 3*M*(1 + epsilon)/(h*N1)
My = MA - HA*y
he = h*epsilon/(1 + epsilon)

Fall 28/19 - case 28/19
Moment am Eckpunkt B
MA = - 3*M*epsilon/(2*N1) + M*epsilon/(2*N2)
MD = - 3*M*epsilon/(2*N1) - M*epsilon/(2*N2)
MB1 = 3*M/(2*N1) + M*epsilon/(2*N2)
MC = 3*M/(2*N1) - M*epsilon/(2*N2)
MB2 = - (M - MB1)
HA = HD = - 3*M*(1+ epsilon)/(2*h*N1)
VA = -VD = M*k*(1+ 4*epsilon)/(l*N2)
My1 = MA - HA*y1
Mx = MC + VD*x'
My2 = MD - HD*y2
E*J1*uB = - (M*h^2)*(1 + epsilon)/(12*N2)

Fall 28/20 - case 28/20
Konsollast am linken Stiel
alpha = a/h
beta = b/h
(alpha + beta = 1)
X1 = 3*P*c*epsilon*[1 + 2*beta*k - 3*(beta^2)*(k +1)]/(2*N1)
X2 = P*c*k*[3*(alpha^2)*(1 + epsilon) - 2*epsilon*(3*alpha -1) - 1]/(2*N1)
X3 = P*c*k*[1+ 2*epsilon*(3*alpha -1)]/(2*N2)
MA = X1 - (0.5*P*c - X3)
MD = X1 + (0.5*P*c - X3)
MB = X2 + X3
MC = X2 - X3
HA = HD = P*c/(2*h) + (X1 - X2)/h
VD = 2*X3/l
VA = P - VD
M1 = MA - HA*a
M2 = MB + HD*b
(M2 - M1 = P*c)
My1 = MA - HA*y1 Bereich a area a
Mx = MC + VD*x' Bereich a area a
My1 = MB + HD*y1' Bereich b area b
My2 = MD - HD*y2 Bereich b area b
E*J1*uB = (h^2)*[X3*(3*k + 1)/k - X2*(2*k + 3)/k - X1 - P*c/2]/6

Fall 28/21 - case 28/21
Konsollast an beiden Stielen, symm
alpha = a/h
beta = b/h
(alpha + beta = 1)
X1 = 3*P*c*epsilon*[1 + 2*beta*k - 3*(beta^2)*(k +1)]/(2*N1)
X2 = P*c*k*[3*(alpha^2)*(1 + epsilon) - 2*epsilon*(3*alpha -1) - 1]/(2*N1)
MA = MD = 3*P*c*epsilon*[1 + 2*beta*k - 3*(beta^2)*(k +1)]/(N1) = 2*X1
MB = MC = P*c*k*[3*(alpha^2)*(1 + epsilon) - 2*epsilon*(3*alpha -1) - 1]/(N1) = 2*X2
VA = VD = P
HA = HD = (P*c + MA - MB)/h
M1 = MA - HA*a
M2 = MB + HD*b
(M2 - M1 = P*c)
My = MA - HA*y Bereich a area a
My = MB + HD*y' Bereich b area b