Of the beam 3613 m mellogeorgia

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Unformatted text preview: DistribuYon of normal stresses is then the same as in pure bending ²་  Advanced theories show that warping due to shear strains does not significantly impact longitudinal strains even when shear force varies conYnuously over the length My ²་  It is therefore jusYfiable to use the flexure formula = for nonuniform bending, I even though formula was derived under the premise of pure bending 3/6/13 M. Mello/Georgia Tech Aerospace 16 EXAMPLE 5- 9 y GIVEN: •  SIMPLY SUPPORTED METAL BEAM: L=1m •  uniform weight (including its own weight: q=28kN/m •  Rectangular cross secYon: b x w = 25mm x 100mm x neutral plane: x- z plane rectangular cross secYon DETERMINE: •  Normal stress σc and shear stress τc at Point C. •  LocaYon of point C: Ø།  25mm below top surface Ø།  100m to the right of support B •  Show these stresses on a sketch of a stress element at point C. SOLUTION: ANTICIPATE THE REQURED FORMULAS x = My I VQ ⌧= Ib 3/4/13 V ⌧= 2I ✓ h2 4 y2 ◆ ✓ 3V ⌧= 1 2A y2 c2 M. Mello/Georgia Tech Aerospace ◆ 17 Example 5- 9: step- by- step soluYon 1.  SOLVE THE STATICS PROBLEM FOR THE REACTION FORCES X X Fv = 0 MA = 0 qL · 0.5m Ay + By = qL kN Ay + By = 28 · 1m = 28kN m By · 1m = 0 By = qL · 0.5m = 14kN Ay By Ay = 14kN 2.  DETERMINE THE SHEAR FORCE DISTRIBUTION WITHIN THE BEAM AT POINT C (or anywhere else within the beam for that ma=er) X L V x V Fv = 0 q (L V = 28 Ay 3/6/13 C Recall sign convenYons for stress resultants x) + Ay = 0 kN · (1m m V = 8.4kN 0.2m) 14kN (V>0, guessed correct sign of shear stress resultant) M. Mello/Georgia Tech Aerospace 18 Example 5- 9: Shear force diagram (cont.) 2.  DETERMINE THE SHEAR FORCE DISTRIBUTION WITHIN THE BEAM AT POINT C (conYnued) AlternaYvely, we may invoke: dV kN = q (x) = 28 dx m V ( x) = kN 28 x + C1 m V integrate 14kN V (0) = Ay = 14kN (leG side b.c.) x = 0.5m x = 0.8m C x kN 8.4kN x + 14kN (shear force funcYon) Ay m kN V (0.8m) = 28 · (0.8m) + 14kN m V (0.8m) = 8.4kN (answer automaYcally provided correct sign of stress resultant) V (x) = 3/6/13 28 M. Mello/Georgia Tech Aerospace 19 Example 5- 9: Bending Moment 3.  DETERMINE THE BENDING MOMENT DISTRIBUTION WITHIN THE BEAM AT POINT C (or anywhere else within the beam for...
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This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Institute of Technology.

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