LECTURE+7+COE-3001-A

2 where ps l 2 e s as the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SMATIC BAR IN TENSION WITH STRESSES ACTING UPON INCLINED SECTION pq. ²་  DECOMPOSE AXIAL FORCE INTO A NORMAL FORCE N (PERPENDICULAR TO THE PLANE) AND SHEAR FORCE V (TANGENTIAL TO THE PLANE) V = P sin ✓ (2-26a,b) N = P cos ✓ ²་  inclined cross- secOonal area: A1 = A/cos✓ ✓ A1 = A/cos✓ 1/17/13 M. Mello/Georgia Tech Aerospace (2-28) (2-28) 25 NORMAL AND SHEAR STRESS SHEAR STRESS COMPONENT NORMAL STRESS COMPONENT ⌧ = V /A1 (2-27b) = N/A1 (2-27a) = N/A1 = P cos ✓ P = cos2 ✓ (A/ cos ✓) A NORMAL STRESS COMPONENT ✓ = cos2 ✓ x ⌧= V /A1 = P sin ✓ cos ✓ A negaOve sign in accordance with sign convenOon i.e., τ>0 when shear force tends produce counter- clockwise rotaOon. SHEAR STRESS COMPONENT 1/17/13 P sin ✓ = (A/ cos ✓) M. Mello/Georgia Tech Aerospace ⌧✓ = x sin ✓ cos ✓ 26 NORMAL AND SHEAR STRESSES (DOUBLE ANGLE FORMS) STRESS ELEMENT ALIGNED WITH xyz axes (Θ=0°) = x ✓ NORMAL STRESS COMPONENT ✓ = x 2 cos2 ✓ ROTATED STRESS ELEMENT ALIGNED WITH FACE OF CROSS- SECTON INCLINED BY ✓ SHEAR STRESS COMPONENT (1 + cos 2✓) (2- 29a) (2-29a) ⌧✓ = ⌧✓ = x x 2 sin ✓ cos ✓ (sin 2✓) (2- 29b) (2-29 ²་  NOTE: EQNS. 2- 29a and 2- 29b derived purely from staOcs. ²་  INDEPENDENT OF MATERIAL PROPERTIES, LINEAR ELASTIC OR NOT! 1/17/13 M. Mello/Georgia Tech Aerospace 27 MAXIMUM NORMAL AND SHEAR STRESSES shear stress maxima at Θ=- 45° max ⌧✓ = normal stress maxima at Θ=0° max ✓ = x x NORMAL STRESS 2 ✓ = x 2 (1 + cos 2✓) (2-29a) SHEAR STRESS ⌧✓ = x 2 (sin 2✓) (2-29b) shear stress “maxima” at Θ=45° 1/17/13 M. Mello/Georgia Tech Aerospace 28 MAXIMUM STRESSES FOR A BAR IN TENSION ²་  Luders’ Bands begin to appear as yield stress is reached ²་  Bands reveal that the material is failing in shear along planes where shear stress is maximum. 45° ELEMENT UNDER MAXIMUM SHEAR STRESS SLIP BANDS (LUDERS’ BANDS) FOR A POLISHED STEEL SAMPLE LOADED IN TENSION (W. LUDERS, 1860) 1/17/13 M. Mello/Georgia Tech Aerospace 29 MAXIMUM STRESSES FOR A BAR IN COMPRESSION 45° ELEMENT UNDER MAXIMUM SHEAR STRESS SHEAR FAILURE ALONG A 45° PLANE IN A BLOCK OF WOOD LOADED IN COMPRESSION 1/17/13 M. Mello/Georgia Tech Aerospace 30 EXAMPLE 2- 9: FAILURE LOAD ANALYSIS OF A COMPRESSION BAR GIVEN: ²་  Compression bar made out of structural plasOc must support P=35kN load ²་  Bar c...
View Full Document

Ask a homework question - tutors are online