6 shearing stresses

6 Shearing Stresses in Beams and Thin-Walled Members

Shearing Stresses in Beams and Thin-Walled Members Introduction Shear on the Horizontal Face of a Beam Element Example 6.01 Determination of the Shearing Stress in a Beam Shearing Stresses t xy in Common Types of Beams Further Discussion of the Distribution of Stresses in a ... Sample Problem 6.2 Longitudinal Shear on a Beam Element of Arbitrary Shape Example 6.04 Shearing Stresses in Thin-Walled Members Plastic Deformations Sample Problem 6.3 Unsymmetric Loading of Thin-Walled Members Example 6.05 Example 6.06

Introduction ,[object Object],[object Object],[object Object],[object Object]

Shear on the Horizontal Face of a Beam Element ,[object Object],[object Object],[object Object],[object Object]

Shear on the Horizontal Face of a Beam Element ,[object Object],[object Object],[object Object]

Example 6.01 A beam is made of three planks, nailed together. Knowing that the spacing between nails is 25 mm and that the vertical shear in the beam is V = 500 N, determine the shear force in each nail. ,[object Object],[object Object],[object Object]

Example 6.01 ,[object Object],[object Object],[object Object]

Determination of the Shearing Stress in a Beam ,[object Object],[object Object],[object Object]

Shearing Stresses  xy in Common Types of Beams ,[object Object],[object Object]

Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam ,[object Object],[object Object],[object Object],[object Object],[object Object]

Sample Problem 6.2 A timber beam is to support the three concentrated loads shown. Knowing that for the grade of timber used, determine the minimum required depth d of the beam. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Sample Problem 6.2 SOLUTION: Develop shear and bending moment diagrams. Identify the maximums.

Sample Problem 6.2 ,[object Object],[object Object],[object Object]

Longitudinal Shear on a Beam Element of Arbitrary Shape ,[object Object],[object Object],[object Object]

Example 6.04 A square box beam is constructed from four planks as shown. Knowing that the spacing between nails is 1.5 in. and the beam is subjected to a vertical shear of magnitude V = 600 lb, determine the shearing force in each nail. ,[object Object],[object Object],[object Object]

Example 6.04 ,[object Object],[object Object],For the upper plank, For the overall beam cross-section, ,[object Object]

Shearing Stresses in Thin-Walled Members ,[object Object],[object Object],[object Object],[object Object],in the flanges in the web ,[object Object]

Shearing Stresses in Thin-Walled Members ,[object Object],[object Object],[object Object]

Shearing Stresses in Thin-Walled Members ,[object Object],[object Object]

Plastic Deformations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Plastic Deformations ,[object Object],[object Object],[object Object],Therefore, the shear stress is zero in the plastic zone. ,[object Object]

Sample Problem 6.3 Knowing that the vertical shear is 50 kips in a W10x68 rolled-steel beam, determine the horizontal shearing stress in the top flange at the point a . ,[object Object],[object Object],[object Object]

Unsymmetric Loading of Thin-Walled Members ,[object Object],[object Object]

Unsymmetric Loading of Thin-Walled Members ,[object Object],[object Object],[object Object]

6 shearing stresses

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