PART 1: STRESS TRANSFORMATION

A wooden beam is loaded with several point forces, as depicted in Fig.1. It is supported by a pin at B and a smooth support (roller) at A. Grains of wood in the beam make an angle of 60° with the horizontal direction. Determine the normal and shear stresses that act perpendicular and parallel to the grains, respectively, at points C and D.

PART 2: STRAIN TRANSFORMATION

A 60° strain rosette is mounted on the surface of a steel bracket to measure the strain state, as shown in Fig. 2. The following readings are obtained for each strain gauge: 𝜀𝜀𝑎𝑎 = −440 × 10−6, 𝜀𝜀𝑏𝑏 = 1120 × 10−6 and 𝜀𝜀𝑐𝑐 = 175 × 10−6. The material properties of the steel bracket are: Young’s modulus E = 200GPa, and Poisson’s ratio ν = 0.3.

(1) Determine the principal strains and the associated orientations.

(2) Determine the maximum in-plane shear strain and the associated normal strain.

(3) Determine the principal stresses and the associated orientations.

PART 3: STATIC DETERMINACY

Classify each of the structures in Fig. 3 as statically determinate, statically indeterminate or unstable. If statically indeterminate, specify the degree of indeterminacy.

PART 4: PLANAR TRUSS ANALYSIS

A truss is loaded with two point forces at its joints, as shown in Fig. 4. Use Method of Joints and/or Method of Sections to obtain the member force for all truss members. State if the members are in tension or compression.

[Hints: You may firstly identify all zero-force members to simplify the truss. Then, use Method
of Joints if at a joint there are only 1 or 2 unknowns. When using Method of Section, choose
the section path so that there are at most 3 unknowns.]