Mae 241 - Lec10

MAE 241 - Statics Summer 2009

Dr. Konstantinos A. Sierros Office Hours: M and W 10:30 – 11:30 (263 ESB new add) [email protected] Teaching Blog: http://wvumechanicsonline.blogspot.com

Determine the force in each member of the truss and state if the members are in tension or compression. Set P1 = 2 kN and P2 = 1.5 kN.

Determine the force in members JI and DE of the K truss. Indicate if the members are in tension or compression.

The truck and the tanker have weights of 8000 lb and 20 000 lb respectively. Their respective centers of gravity are located at points G1 and G2 . If the truck is at rest, determine the reactions on both wheels at A, at B, and at C. The tanker is connected to the truck at the turntable D which acts as a pin.

Chapter 7: Internal forces Chapter objectives • Use the method of sections to determine internal loadings in a member • Generalize the procedure in order to formulate equations that can be plotted to describe internal shear and moment throughout a member • Analysis of forces and geometry of cables supporting a load

7.1 Internal forces developed in structural members •To design a structural or mechanical member it is necessary to know the loading acting within a member in order to make sure the material can resist this loading • Internal loadings can be determined by using the method of sections • Use section B, separate the beam into two segments. The internal loadings acting at B will then become external

7.1 Internal forces developed in structural members

7.1 Internal forces developed in structural members • NB acts perpendicular to the cross-section and is termed the normal force • VB is tangent to the cross-section and is called shear force • MB is bending moment • The force components prevent the relative translation between the two segments. The couple moment prevents the relative rotation • When analysing forces/moments the right segment is the better choice since it doesn’t involve the unknown reactions at A

7.1 Internal forces developed in structural members • NB is found by ΣFx = 0 • VB is obtained using ΣFy = 0 • MB is obtained by applying ΣMB = 0 (Moments of NB and VB about B is zero

7.1 Internal forces developed in structural members

Normal force (N) is positive when creates tension A positive shear force (V) will rotate the segment clockwise A positive bending moment will tend to bend the segment in a concave upward manner (smiley face)

7.2 Shear and moment equations and diagrams • Beams are structural members designed to support loadings applied perpendicular to their axes • Simply supported beam is pinned at one end and roller supported at the other • Detailed knowledge of the variation of the internal shear force V and bending moment M along the beam axis • Using the method of sections we can find these variations

7.2 Shear and moment equations and diagrams Construction of bending-moment diagrams 2. Support reactions 3. Shear and moment functions 4. Plot shear and moment diagrams