Material: Steel S 235 (former St 37)
circular cross section, radius r = 2 mm |
usual steel in machine industrie and steel construction with moderate load |
| Elastic modulus E |
E = 210000 N/mm2 |
| Area moment IF, circular cross section, d = 4mm |
IF = p · r4 / 4 =
12,566 mm4
|
| Tensile strength Rm |
Rm = 340 N/mm2 |
Yield point Rp 0,2
after total discharge remains a plastic
strech of 0,2%
|
Rp 0,2 = 235 N/mm2 |
| Equivalent factors for steel |
k1 = 0,5, k2 = 1,4 for bending
k1 = 0,3, k2 = 0,58 for torsion |
| Bending moment Mb for one-sided bearing |
Mb = F · l |
Section modulus W
for circular cross section, r = 2 mm |
W = p · r3 / 4 =
6,283 mm3
|
| Bending stress sb |
sb = Mb / W |
| Bending moment Mb for double sided movable bearing |
Mb = F · l / 4 |
| Torsional moment Mt | Mt = F · r |
Polar section modulus Wp
for circular cross section, r = 2 mm |
Wp = p · r3 / 2 =
12,566 mm3
|
| Torsional stress tb |
tt = Mt / Wp |
| Equivalent stress sv |
sv =
Ö[sb2 +
3(a0 · tt)
2] mit a0
» 0,7
|
Assumed limits for bending stress sb zul
according to the fatigue strength diagram |
sb zul = k2 · Rp 0,2 = 330 N/mm2
for static bending
sb zul =
ssch =
255 N/mm2 for swelling bending
sb zul = k1 · Rm
= 170 N/mm2
for alternating bending
|
Assumed limits for torsional stress tt zul
according to the fatigue strength diagram |
tt zul = k2 · Rp 0,2 = 135 N/mm2
for static torsion
tt zul =
tsch =
135 N/mm2 for swelling torsion
tt zul = k1 · Rm
= 100 N/mm2
for alternating torsion
|
Required torque M to accelerate a vehicle
with the mass m on a flat bottom from zero speed
to a velocity v within the time t by means of wheels
with radius R
|
M = F · R = m · a · R = (m · v · R) / t |
Fatigue strength diagram for bending
|
Fatigue strength diagram for torsion
|
