Combined Stresses –Combined Normal Stresses Axial(P)/Bending (M) Page A 1

Calculate tensile stress

Calculate bending stress

Find total

708

10 k

30o

Combined Stresses –Combined Normal Stresses Axial(P)/Bending (M) Page A 2

10.6 page 588 Tension in blade is 125 N Draw free-body of top beam

Find compressive stress

Find bending stress

Find combined worst case

Combined Stresses –Combined Normal Stresses Axial(P)/Bending (M) Page A 3

10.16 page 590 EF Tensile 54 kBack to back steel angles, ASTM A360.6 yield strength Pg 696 angles

Try 4 x 3 x 1/4

Free-body of EF

Shear Diagram

Moment Diagram

Populate

σ= P2 A

+ M2S

Estimate need A for axial only

Estimate needed S for bending only

Combined Stresses – Combined Normal and Torsional Shear Stress Page B 1

10-28 page 592-3Choose standard pipeHold Maximum Shear stress to 8000psi

Identify worst case element

Find M on element

Find T on element

Select pipe page 710 Find ZP needed

Combined Stresses – Rotating Shafts, Page C 1

Page 546 - 55110.32 page 594, shaft diameter 1.75 inFind maximum shear stress

3. Sketch torques at each pulley

1. Find y force at bearings

2. Sketch shear and moment diagrams

4. Find τmax at C

τ max=√(σ2 )2

+τ2

Combined Stresses – Axial/Direct Shear Page D 1

xy

10-40 page 595Machine screw diameter 48 mm, pitch 5.0mm page 694Tensile stress 120 MPa on thread tensile areaNon treaded area pure shear force of 80kN.Find the maximum shear stress

Find force Find τ

Find combined

Find σ at element

Noncircular Shapes Page F 1

Page 227 use Roark for other shapes

10-46 page 595 Triangle 50mm sidesAxial force 115 kNTorque 775 NmFind maximum shear stress.

Find σ

Find τ

Find τmax

General Combined Stresses Page G 1

10.60 page 597σx = 20 ksi σy -5 ksi τxy 10 ksi CCWmaximum shear stresscalculate principal stresses

τ max=∓ √[ 12 (σx−σ y )]

2

+τ xy2

σ 1=12 (σ x+σ y )+ τmax

σ 2=12 (σ x+σ y )−τmax

General Combined Stresses Page G 2

Normal stress in u direction

σ u=12 (σ x+σ y )+ 1

2 (σx−σ y ) cos2φ−τ xy sin2φ

Shear stress, uv

τuv=−12 (σ x−σ y ) sin 2φ−τ xycos2φ

10-96 page 598σx = 300 MPa, σy = -100 MPa, τxy = 80 MPa cw30 deg ccw

General Combined Stresses – Mohr’s Circle Page H 1

10.60 page 597σx = 20 ksi σy -5 ksi τxy 10 ksi CCWUse Mohr’s circle to find principal stressesmaximum shear stress

Plot σx and τxy, σy and τyx

Use circle geometry instead of equations

CW

General Combined Stresses – Mohr’s Circle Page H 2

10-92 page 598σx = -840 kPa σy -335 kPa τxy 120 kPa CCWUse Mohr’s circle to find principal stressesmaximum shear stress (enhanced)

Combined Stress Design Page G 1

Steps (stay in N and mm for stress calculations)Find σ from bending

σ x=K tM cI

=K tMS

Find τ from torque

τ xy=K tTcJ

=K tTZ P

Find σ1 σ2 τmax using equations or Mohr’s circleCompare to τmax guideline and material propertyFind Von Mises σe Compare to guideline and material property

Study pages 528 - 540

Power shaft, AISI 1040 cold drawn, 55mm diameter, Kt = 1.6, TB = 298 Nm, N = 4Will it fail using maximum shear stress failure theory?Will it fail using Von Mises failure theory?

Combined Stress Design Page G 2

Combined Stress Design Page G 3

Combined Stress Design Page G 4