came1pt3 - the plane of the joint are P.cos( θ ) and...

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Question1.3: A square prismatic bar of 1300-sq.mm cross-sectional area is composed of two pieces of wood glued together along the x’ plane, which makes an angle θ with the axial direction. The normal and the shearing stresses acting simultaneously on the joint are limited to 20 and 10 Mpa, respectively, and on the bar itself, to 56 and 28 Mpa respectively. Determine the maximum allowable axial load that the bar can carry and the corresponding value of angle θ . Y Solution Y’ X’ X θ P P Let us denote the axial force applied by “P”, the cross-sectional area of the bar by “A”, σ , σ ’, τ , τ ’ be the normal and shear stresses on the normal cross-section of the bar and the joint respectively. Cross-section of the joint, ) cos( A A' q = ………………. by geometry. Now the stresses developed on the joint are ' joint on the force Normal ' A = s ' joint on the force shear ' A = t Since the axial load on the bar is P, the normal and shear components of this load onto
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Unformatted text preview: the plane of the joint are P.cos( θ ) and P.sin( θ ) respectively. Hence, ' P.cos ' A q s = ' P.sin ' A q t = Substituting the value of A’, we get ' cos P. ' 2 A q s = MPa allowable 20 = s Q MPa A 20 ' cos P. 2 = ∴ q ∴ P.cos 2 ( θ ) = 20 x1300……….(1) And, ' sin . cos P. ' A q q t = MPa allowable 10 = t Q MPa A 20 ' sin . cos P. = ∴ q q ∴ P.sin( θ ) .Cos( θ ) = 10 x1300……….(2) Dividing (2) by (1), we have, Tan( θ ) = 0.5 Which gives θ = 26.56 0 Now, We put back the value of θ in (1) to get ) 56 . 26 ( cos 1300 20 2 × = ∴ P ∴ P = 32500 N ∴ P = 32.5 KN Now, we check whether the stresses induced in the bar are within safe limits 1300 32500 = s ∴σ = 25 Mpa < 56 Mpa, hence, safe 1300 2 32500 × = t ∴τ = 12.5 Map < 28 Mpa, hence, safe. Final Answer The maximum allowable axial load that the bar can carry is 32.5 KN and the corresponding value of the angle is 26.56 degrees....
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This note was uploaded on 11/22/2011 for the course EML 6653 taught by Professor Law during the Fall '09 term at University of South Florida - Tampa.

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came1pt3 - the plane of the joint are P.cos( θ ) and...

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