STD MODULE 7 - Design and Investigation of Steel Beams and Girders

1. Bending Stress

2. Shear Stress

3. Deflection

Beams/Members subject to Bending for STEEL (similar sa timber)

1. Bending Stress

2. Shear Stress

3. Deflection

4. Axial Stress

Axially loaded members (if Columns and Truss Members)

Axial Load

Load transmitted along longitudinal section

σb = M/S

M = bending moment (N·mm or kN·m)

S = Section Modulus of the section for rectangular beams

General Bending Stress formula

σb = 6M / bd^2

σb​ = Bending stress (MPa)

M = Bending moment (N·mm or kN·m)

b = Width of the beam (mm)

d = Depth (height) of the beam (mm)

Bending stress formula (for a rectangular beam section)

t = 3V/2bd

𝜏​ = Shear stress (MPa)

V = Shear moment (N·mm or kN·m)

b = Width of the beam (mm)

d = Depth (height) of the beam (mm)

Shear Stress formula

1. d = 5wL^4 / 384 EI (Uniform Load)

2. d = PL^3 / 48 EI (Concentrated Load)

Deflection formula

Fb = 0.66 Fy

Compact Section

Fb = 0.60 Fy

Non-Compact Section

Fv = 0.40 Fy

Allowable Shear Stress

1. width of flange, mm

2. depth of section, mm.

3. thickness of flange, mm

4. tw thickness of web, mm.

5. yield stress , Mpa

Fill in the blanks:

1. bf = ___________________

2. d = __________________

3. tf = __________________

4. tw = __________________

5. Fy = __________________

T

T/F: ALL three criteria (check ppt) must be met in order for a section be considered as Compact.

Local Flange Buckling

1st and 2nd Criteria: Flange width (d) with Flange thickness (tf)

If the ratio of bf to tf is greater than the prescribed limit, there is a possibility of the occurrence of ___________________ which could affect the overall strength of the section

Web Crippling

Third Criteria: Ratio of d (depth) with tw (web thickness)

If the ratio of d to tw is greater than the prescribed limit, there is a possibility of the occurrence of _______________ .

shear carrying capacity

Web Crippling can also affect the __________________ of the section. Thus this is also checked with a prescribed limit to determine the allowable shear stress.