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SECOND YEARSUB. RESISTANCE OF

MATERIALS

MSc. Ashraf A. M. R. Hiswa

2013

UNIVERSITY OF KUFAFACULTY OF ENGINEERING CIVIL DEPARTMENT

Outlines

Stress Concept Types of Stresses Applications on Stress Design of Materials Due to Stress

Capacities

Stress Concept

Stress is the distribution of a force throughout the cross-sectional area of a structural member

Types of Stresses

1- Normal / Direct Stress

It is product of a force normal

to the area.

σ = Where:-

σ: Direct stress, F: force, A: cross-sectional area = h*w

Types of Stresses

=

=

=

Sign Convention

UnitsStress = = = Pa., = = = 106 Pa. = MPa

Applications on Stress

Ex.1/ Calculate the stress due to the applied load if the cross section is rectangle with width of (20 mm) and height of (30 mm).

Sol./

F = 60 kN (com.)

A = 20*30 = 600 mm2

σ = = = - 600 MPa.

Types of Stresses

2- Shear Stress

It is product of a force normal

to the area.

= Where:-

: Shear stress, F: force, A: cross-sectional area = h*w

Types of Stresses

: Shear stress due to force in the y-direction acts on the area normal to x-direction.

=

Sign Convention

- τ + τ

UnitsStress = = = Pa., = = = 106 Pa. = MPa.

Applications on Stress

Ex.2/ Calculate the shear stress induced in the bolt due to the applied loads if diameter of the bolt is 10 mm.

Sol./F = 80 kN

A = 2* = 2* * 102/4 = 157 mm2

τ = = = ) 509.55 MPa.)

Design of Materials Due to Stress Capacities

For Direct Stress

≤

For Shear Stress

≤

Where;

, : Direct and Shear Stresses due to applied loads.

, : Direct and Shear Resistance Stresses of Material.

Applications on Stress

Ex. 3/ the frame below was supposed by an engineer to support the distributed load (w=20 kN/m) over the carrier which is supported by cable from one side and a platform from the other side, calculate the cable diameter, the carrier height (h) and the required distance from the carrier to be supported by the platform (x) if you know that tension capacity of the cable is (400 MPa.) and the compression and shear resistance of the carrier are (400 MPa.), (200MPa.) respectively.

Applications on Stress

Sol. /

According to the equilibrium law

Force on platform = force in cable = 20*5/2 = 50 kN = 50000 N

-Design of Cable

≤ → ≤ 400 MP. → ≤ 400 → = 125 mm2 ≤ A

125 ≤ D2/4 → D ≥ 12.6 mm → use cable of diameter of (13 mm).

-Design of carrier

Shear force = compression force = 50 kN. (for carrier at platform)

Calculation of (x)

≤ → ≤ 400 MP. → ≤ 400 → = 125 mm2 ≤ A

125 ≤ 10*x → x ≥ 12.5 mm → use x=13 mm.

Calculation of (h)

≤ → ≤ 200 MP. → ≤ 200 → = 250 mm2 ≤ A

250 ≤ 10*h → h ≥ 25 mm → use h =30 mm.

References

Megson, T. H. G. (1996). STRUCTURAL AND STRESS ANALYSIS. Oxford: Butterworth-Heinemann.

Saad, M. H. (2005). ELASTICITY Theory, Applications, and Numerics. Oxford: Butterworth-Heinemann.

Hosford, W. F. (2005). Mechanical Behavior of Materials. New York: Cambridge University Press.