CE 201 - Statics

1. CE 201 - Statics Chapter 7 – Lecture 1

2. INTERNAL FORCES • Internal Forces Developed in Structural Members (2-D) • Internal Forces Developed in Structural Members (3-D)

3. Internal Forces Developed in Structural Members (2-D) • To design a member, the forces acting within the member need to be determined. These forces are known as the internal forces and can be found by using the method of sections. • The method can be illustrated by the following example.

4. F1 F2 A B C F1 F2 Ax B A C By Ay The reactive forces at the supports (A) and (B) can be determined by applying the Equilibrium Equations (Fx = 0; Fy = 0; Mo = 0) on the entire structure.

5. F1 F2 Ax B A F2 C By Ay B By F1 Ax A C C Ay Suppose that the forces acting at (C) are to be found, then it is necessary to make a section at (C).

6. F1 F2 VC VC MC MC Ax NC NC B A C By Ay C NC VC MC These external forces and couple moment will develop at the cut section in order to prevent the segments from translating or rotating Nis called the normal force V is called the shear force M is called the bending moment or couple moment Note: VC, NC, and MC on both segments are equal in magnitude and opposite in direction. VC, NC, and MC can be determined by applying the equilibrium equations (Fx = 0; Fy = 0; Mo = 0) on one of the segments.

7. F1 F2 VC VC MC MC Ax NC NC B A C By Ay C Internal Forces developed in Structural Membranes (3-D)

8. z Vz Mz y Ny C My Mx Vx x • Ny is normal to the cross-sectional area. • Vx and Vz are components of the shear force and they are acting tangent to the section. • My is the torsional moment or twisting moment. • Mx and Mz are components of the bending moment. • The resultant loadings (forces and moments) act at the centroid of the cross-sectional area.

9. Procedure for Analysis • Support Reactions (before cutting) • Free-body Diagram (of the segment that has the least number of loadings) • Equilibrium Equations