do BeamsCity in Germany: Step-by- step Przykłady:
Obliczanie bending stress in beams is essential in structural inserering to ensure safety andd performance. This process involves understang the forces acting on a beem and how they translate into internal stresses. The following guides provides a step approvach with practical examples to to quanfy the callations involved.
Understanding Bending Stress
Bending stress evens when a momento causes a beum to bend. It i s difficed across the cross- section, with the maximum stres typically athe outermost fibers. The formula for bending stress is:
Xi1; Xi1; FLT: 0 Xi3; Xi3; В = (M * y) / I Xi1; Xi1; FLT: 1 Xi3; Xi3; Xi3;
Kiedy:
- Xi1; Xi1; FLT: 0 Xi3; Xi3; Xi1; Xi1; FLT: 1 Xi3; Xi3; = stresy bendinga
- = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
- (zob. pkt 2.1.1.1 niniejszego załącznika)
- Xi1; Xi1; FLT: 0 Xi3; Xi3; I Xi1; Xi1; FLT: 1 Xi3; Xi3; = moment of inertia of the cros- section
Etap - by- Stopień obliczenia
First, determinate the bending momento at te point of interest. Next, identify the cross- sectional properties, including the momento of inertia and the e distance to o thee outer fiber. Substitute these values into the formula to find the bending stres.
Badanie Calculation
Uproszczony, wspierany przez beat with a span of 6 meters caries a uniform load of 10 kN / m. Tu znajduje się ten maximum bending stress at te center:
Te maximum bending momento is:
Xi1; Xi1; FLT: 0 Xi3; Xi3; M = (w * L ^ 2) / 8 = (10 * 6 ^ 2) / 8 = 45 kNm Xi1; Xi1; FLT: 1 Xi3; Xi3;
Załóżmy, że prostokąty skrzyżowania-section with a width of 200 mm andhigt of 300 mm, thee momento of inertia is:
(b * h ^ 3) / 12 = (0, 2 * 0, 3 ^ 3) / 12 = 4, 5 * 10 ^ - 3 m ^ 4
Te dystance to te outer fiber is:
(zob. pkt 2.1.1.1 niniejszego załącznika)
Obliczanie tej siły bending:
Xi1; Xi1; FLT: 0 Xi3; Xi3; В = (M * y) / I = (45 * 10 ^ 3 * 0.15) / 4.5 * 10 ^ -3 = 1.5 * 10 ^ 8 Pa Xi1; Xi1; FLT: 1 Xi3; Xi3;
To maximum bendim stress is approximately 150 MPa.