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Unformatted text preview: cross secRon at posi(on y’ from NA. x
y
y
• Q is the Moment of Area of A’ about NA: y
x
x SuperposiRon of Stresses y Mz
P
• Stresses may only be added if they are applied over the same x
y
area, and act along the same direcRon. •
Mz Normal Stress and Shear Stress components are not added P
x
together. Mz
P
• Sum normal axial and bending stresses for this simple example: y
P y
yx Axial Stress Bending Stress x
x Combined Stress Combined Stresses Procedure • IdenRfy the points of interest where stresses are to be calculated. • Take a secRon through each point and construct FBDs. • The internal reacRons at the centroid of each secRon must be found from equilibrium. • Calculate the stress components caused by each internal reacRon component. • Superimpose stresses appropriately and sketch normal and shear stresses on a properly oriented element. 11 42) Two designs for a beam are to be considered. Determine which one will support a moment of M = 150 kN ༉ m with the least amount of bending stress. What is that stress? Hibbeler 4th ed 200 mm 200 mm 30 mm 15 mm 300 mm
30 mm 300 mm
15 mm 15 mm
(a) 30 mm
(b) Given: design load and two possible cross secRons. Find: opRmum cross secRon for minimum stress, value of the stress. Plan: apply the ﬂexure formula to both cross secRons and compare stress calculaRons. 11 42) Hibbeler 4th ed (a): (b): 30 mm 15 mm 300 mm
30 mm To minimize σmax, we need to maximize I/c. I/c is called the Sec(on Modulus: 200 mm 200 mm 300 mm
15 mm 15 mm
(a) 30 mm
(b) 11 42) Hibbeler 4th ed (a): (b): 30 mm 15 mm 300 mm
30 mm To minimize σmax, we need to maximize I/c. I/c is called the Sec(on Modulus: 200 mm 200 mm 300 mm
15 mm 15 mm
(a) 30 mm
(b) Use cross secRon (b) 12 24) Determine the maximum shear stress in the T beam at the criRcal secRon where the internal shear force is maximum. 10 kN / m Hibbeler 4th ed A B C 1.5 m 3m 1.5 m 150 mm 150 mm 30 mm
30 mm Given: load and beam dimensions. Find: τmax Plan: Construct shear diagram to ﬁnd max V then apply the shear formula to ﬁnd the max shear stress. Max shear on the cross secRon occurs where Q/t is max, which should be at the NA of this T beam. We must ﬁnd posiRon of NA. 12 24) FBD: 10 kN / m Hibbeler 4th ed 1.5 m 30 kN 15 kN 10 kN/m A 1.5 m 3m B C 1.5 m 150 mm Ay 4m 2m 10 kN/m
3m By 27.5 kN150 mm 3m
30 mm 17.5 kN 30 mm 3m 3m...
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 Winter '08
 OSAMA

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