Structure I Course Code: ARCH 208 Dr. Aeid A. Abdulrazeg Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 5.1,5.2

Equations of Equilibrium For equilibrium: For most structures, it can be reduced to:

Determinacy & Stability Equilibrium eqns provide sufficient conditions for equilibrium All forces can be determined strictly from these eqns No. of unknown forces > equilibrium eqn => statically indeterminate This can be determined using a free body diagram

Determinacy & Stability For a coplanar structure The additional eqns needed to solve for the unknown eqns are referred to as compatibility eqns

Example 1 Classify each of the beams shown in Fig 1 as statically determinate or statically indeterminate If statically indeterminate, report the no. of degree of indeterminacy The beams are subjected to external loadings that are assumed to be known & can act anywhere on the beams

Applications of the Equations of Equilibrium (Beams) Example 2 Determine the reactions on the beam shown in Fig 270kN 0.3 m 6.8 kN.m 3 m 1.2m 2.1 m Plan: the 270 kN force is resolved into x & y components. Draw a complete FBD of the boom. 3. Apply the E-of-E to solve for the unknowns.

270kN 0.3 m 6.8 kN.m 3 m 1.2m 2.1 m 270 Sin 60o 0.3 m 6.8 kN.m 270 Cos 60o 3 m 1.2m Free Body Diagram

Example 3 The compound beam in Fig is fixed at A Determine the reactions at A, B & C Assume the connections at B is a pin & C a roller

Free Body Diagram

solution There are 6 unknowns, applying the 6 eqns of equilibrium, we have:

GROUP PROBLEM SOLVING (Continued) Example 4 Determine the reactions on the beam in Fig. Free Body Diagram

Determine the reactions on the beam. Assume A is a pin PROBLEM (Continued) Example 5 Determine the reactions on the beam. Assume A is a pin and the support at B is a roller (smooth surface). 10 kN/m 4 m 6 m 3 m Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 5.1,5.2