Table of Contents
Flexural according to AISC codes. These calculations ensure safety and complicance in structural design. Real- examples ilustrate how accordery these principles in practice.
Example 1: SimpleBeam Under Uniform Load
A steel beam with a span of 6 meters is subjected to a uniform dead of 10 kN / m. Te beam 's cross- section is a W- shaped section with a moment of inertia (I) of 1500 cm decd of 1; FLT: 0 cm 3; FLT 3; 4 crr 1; FLT: 1 crr 3; The goal is to verify if the beam cam can with stand e bending moment.
Te maximum bending moment (M) for a simployy supported beam under uniform headd is calculated as:
M = (w * L CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS3;) / 8
Where w = 10 kN / m and L = 6 m, so:
M = (10 * 6); FL1; FLT: 0 (3m); FL1; FL1; FLT: 1 (3m); FL3m / 8 = 45 kNm
Using AISC formulas, thee applid section modulus (S) is calculated as:
S = M / Fy
Assuming Fy = 250 Mpa, then:
S = 45,000 / 250 = 180 cm (1; 1; FLT: 0; FLT: 3; 3; FLT: 1; FLT: 1; FLT; 3;
Te selected section 's S exceeds thee applicd value, indicating consistacy.
Example 2: Bending Stress Check
A steel beam with a obdélníkový cross- section (width 200 mm, hight 300 mm) is supported over a 5-meter span. It carries a concentrated chesd of 20 kN at mid- span. Thee engineer ness to o verify thee bending stress.
Te maximum bending moment (M) at mid- span is:
M = (P * L) / 4 = (20 * 5) / 4 = 25 kNm
Te section modulus (S) for a obdélníku section is:
S = (b * h PHARMA1; FL1; FLT: 0 PHARMAD 3; PHARMAD 3; 2 GARMAD 1; GARMAD 1; FLT: 1 GARMAD 3; PHARMAD 3;) / 6
Calculating S:
S = (0, 2 * 0, 3 * 1; FLT: 0 CLAS3; FLAS3; 2 CLAS1; FLAS1; FLAS3;) / 6 = 0, 003 m CLAS1; FLAS1; FLAS1; 3 CLAS1; FLAS1; FLT: 3 CLAS3; OR 3000 cm CLAS1; FLAS1; FLAS3; FLAS3; 3 CLAS3; FLAS1; FLAS1; FLAS3; FLAS3;
Te bending stress (К) is:
(25,000 * 10) / 3000 = 8,33 Mpa
To je to, co je možné, že je to limit (např. 250 Mpa), to je suable for to e chead.
Example 3: Shear Force and Shear Stress
A steel beam spans 8 meters and supports a point deadd of 50 kN at mid- span. Te cross- section is a I-beam with a web houstness of 8 mm. Thee engineer checs shear capacity.
Te maximum shear force (V) at mid- span is equal to te te chead:
V = 50 kN
Te shear stress (τ) in thee web is calculated as:
τ = V / A CLAS1; CLAS1; CLAS3; CLAS3; CLAS3;
Where A CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; web CLAS1; CLAS1; FLT: 1 CLAS3; CLAS3; = web area = web contenness * web height.
A CLAS1; CLAS1; CLAS3; CLAS3; web CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS1; CLAS1; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS33; CLAS3S3;
τ = 50,000 N / 0, 0024 m CLAS1; CLAS1; FLT: 0 CLAS3; CLAS3; 2 CLAS1; CLAS1; FLT: 1 CLAS3; CLAS3; CLAS3; CLAS31; CLAS33 Mpa
Eventue thee shear stress is below thee web 's shear capacity (např., 250 Mpa), thee beam' s web is conditate.