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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.