If a = 8 in. , locate the centroid y¯of the cross-sectional area of the built-up beam.

B.2. Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: σ, X (M.1, M,1,)y+ (M, I. - M.1,-) z (1,1.-1²-) where My and M₂ are bending moments applied to a cross-section, and where ly, Iz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (i) What assumptions have been made in the derivation of the above expression? (ii) Indicate by means of a sketch the directions in which positive values of the bending moments My and M₂ act on a cut plane facing in the positive x direction.

For the beam with coordinate shown in figure. Develop the flexibility matrix. 1 L 2 C 12 B

Consider the rod shown. Suppose that hℎ = 170 mm, r = 290 mm. Determine the location (x,y)  of the centroid of the rod.

Q1: Solve Determine a scalar d so that the angle between A=2i+4j and B = 9itdj is 45°.

STRENGTH OF MATERIALS (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG EXPLANATION NEEDED. ANSWER IN 3 DECIMAL PLACES.)

Find OF ģ, C, I, A', ğ,b the value A' = area above axis = the distance fom the center of A to the centroidal moment OF Iner tia b = the centroidal axiis base OF are a above attached tロ C = the distance From tne center to the topmost Fiber OF the bcam Formulas: Fb= Mc Ib Fb=bending stress v: shearing stress M = max value OF moment N= ma* value OF shear : E ay AT O.0amm O.004mm 0.02mnm 0.12 m m

Problem 1: Determine the forces in all members of the truss shown below. 2m B 45% 45 2m 45% с 4m 45% D r = 0.5m 30* 3 kN

Can

The cross-sectional dimensions of a beam are shown. Assume b-1.875 in., t-tw-0.125 in. and d=2.75 in. (a) If the bending stress at point K is 3340 psi (T), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress o, at point H (positive if tension, negative if compression). H K Answers: bf (a) M₂ = i (b) σH = tw lb-ft. psi.