Mechanics of Materials CIVL 3322 / MECH 3322

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Gillian Lane
5 years ago
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1 Mechanics of Materials CIVL 3322 / MECH

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9 In Statics, we spent most of our time looking at reactions at supports Two variations from this were when we considered the forces in trusses and The shear and moment at a point in a beam (you may or may not have looked at this) 17 In Mechanics of Materials, it is these internal forces and how they affect the behavior of the system that will be critical to our analysis Depending on the loading pattern, there can vary greatly through the beam 18

10 19 At any point in a continuous system, we can look at the internal forces acting on the system by modeling the point we are looking at in the system as a fixed end support. 20 This means that at any point in a continuous member, we will have a force parallel to the member, a force perpendicular to the member and a resistive moment.

11 The force that acts parallel to the cut we make to separate the member is known as the axial force or the normal force The force that acts perpendicular to the cut is known as the shear force The moment is known as the bending moment 21 22

12 23 The dark blue arrows along the axis of the beam are the axial forces The axial force is considered as a positive axial force if it would cause the section under consideration to be in tension. The axial force is considered as a negative axial force if it would cause the section under consideration to be in compression. 24

13 25 This shear force is always normal to the axis of the cut face of the beam and is typically labeled as V. The force acting on the plane of the cut generates a stress on that plane If the force is normal to the plane, the stress is a normal stress or an axial stress If the force is parallel to the plane, the stress is a shear stress 26

14 The magnitude of the stress is the ratio of the magnitude of the applied force to the area of the cross section For normal stress, the expression is σ avg 27 F = A This expression assumes that the force is equally distributed across the cut face To determine the axial stress at a point required an ability to divide the force according to some function σ avg 28 F = A

15 Units of stress are similar to units of pressure Lbf/ft2 l N/m2 l A N/m2 is given the unit of Pa (Pascal) σ avg 29 F = A Pressure is a scalar, stress is a vector so they are not exactly the same Usually you don t see Pa by itself, the units are KPa, MPa, GPa σ avg 30 F = A

16 Pressure is a scalar, stress is a vector so they are not exactly the same Usually you don t see Pa by itself, the units are KPa, MPa, GPa 31 A solid 0.5 in diameter steel hanger rod is used to hold up one end of a walkway support beam. The force carried by the rod is 5,000 lb. Determine the normal stress in the rod. (Disregard the weight of the rod). E01

(b) If the maximum normal stress in member (1) must be limited to 50 Mpa, what is the maximum load magnitude P that may be applied to the rigid

17 Rigid bar ABC is supported by a pin at A and axial member (1), which has a cross section of 540 mm2. The weight of the rigid bad ABC can be neglected. (a) Determine the normal stress in member (1) is a load P=8kN is applied at C. (b) If the maximum normal stress in member (1) must be limited to 50 Mpa, what is the maximum load magnitude P that may be applied to the rigid bar at C? A 50-mm-wide steel bar has axial loads applied at points B, C, and D. If the normal stress magnitude in the bar must not exceed 60 MPa, determine the minimum thickness that can be used for the bar.

Determine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.

E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct