1. 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
= x106 mm4

2. = + 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

3. 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 = – = 1.5 Mpa (tensile)
Maximum bending stress at the lower part of the beam:
s = –0.3 – 1.8 = –2.1 MPa (compressive)

4. 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

5. 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

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

7. 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.

8. 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)

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