PROBLEM-1 500 mm x y 800 mm P = 1500 N z y 50 mm 100 mm The solid rectangular beam shown has a cross-sectional area 100x50 mm. If it is subjected to the loading shown, determine the maximum stress in segment BC. Cross-sectional area: A = (50)(100) = 5000 mm2 Moment of inertia: I = = bh3 12 (50)(100)3 = 4.167x106 mm4

= + PROBLEM-1 y x y x Stress components in segment BC: Axial Load (negative) Bending (negative) M = – P(500) N.mm = – 750 kN.mm x 500 mm P = 1500 N 800 mm Stress components in segment BC: 1. Compressive stress due to axial load: s = – P/A = –1500/5000 = –0.3 N/mm2 s = –0.3MPa 2. Bending stress: s =  =  =  1.8 N/mm2 Mc I (–750x103)(50) 4.167x106 s = 1.8 MPa s = –1.8 MPa

PROBLEM-1 500 mm x y 800 mm P = 1500 N = x y + P M Axial Load (negative) Bending (negative) M = – P(500) N.mm = – 750 kN.mm s = –0.3MPa s = 1.5 MPa s = –2.1 MPa = s = 1.8 MPa s = –1.8 MPa + Maximum bending stress at the upper part of the beam: s = – 0.3 + 1.8 = 1.5 Mpa (tensile) Maximum bending stress at the lower part of the beam: s = –0.3 – 1.8 = –2.1 MPa (compressive)

PROBLEM-2 T Stress in Shaft due to Bending Load and Torsion A shaft has a diameter of 4 cm. The cutting section shows in the figure is subjected to a bending moment of 2 kNm and a torque of 2.5 kNm. T x y z Determine: The critical point of the section The stress state of the critical point. FG09_23c.TIF Notes: Example 9-12: solution

Analysis to identify the critical point PROBLEM-2 Analysis to identify the critical point Due to the torque T T x y z Maximum shear stresses occur at the peripheral of the section or on the outer surface of the shaft. Due to the bending moment M FG09_23c.TIF Notes: Example 9-12: solution A Maximum tensile stress occurs at the bottom point (A) of the section. Conclusion: the bottom point (A) is the critical point

PROBLEM-2 T Stress components at point A Due to the torque T x y z Stress components at point A Due to the torque T 198.94 MPa A Due to the bending moment M FG09_23c.TIF Notes: Example 9-12: solution 318.31 MPa 318.31 MPa 198.94 MPa Stress state at critical point A sx = 318.31 MPa txy = 198.94 MPa

PROBLEM-3 Stress in Shafts Due to Axial Load, Bending and Torsion A shaft has a diameter of 4 cm. The cutting section shows in the figure is subjected to a compressive force of 2500 N, a bending moment of 800 Nm and a torque of 1500 Nm. FG09_17c.TIF Notes: Procedure for Analysis Determine the stress state of point A.

PROBLEM-3 Analysis of the stress components at point A Due to comprsv load: Due to torsional load: FG09_17c.TIF Notes: Procedure for Analysis Due to bending load: (compressive stress)

PROBLEM-3 txy sx Stress state at point A Shear stress: txy = tA = 119.37 MPa Normal stress: sx = sA’ + sA” = (– 1.99 – 127.32) MPa = – 129.31 MPa FG09_17c.TIF Notes: Procedure for Analysis