3. For the beam and loading shown, use singularity functions to determine (a) the equation of the elastic curve, (b) the slope at A, and (c) the maximum deflection.

For the wire form shown, use Castigliano's method to determine the deflec- tion of point A in the y direction. Consider the effects of bending and torsion only. Use the straight beam formulation for the bending energy. The wire is steel with E 200 GPa, v = 0.29, and has a diameter of 5 mm. Before cation of the 200-N force the wire form is in the xz plane 100 mm. = appli- where the radius R is

For the beam and loading shown, use discontinuity functions to compute: (a) the deflection VA of the beam at A, and (b) the deflection Vmidspan of the beam at midspan (i.e., x = 2.45 m). Assume a constant value of El = 1270 kN-m² for the beam; M₁ = 9 kN-m, wo = 19.8 kN/m, LAB = 1.1 m, LBc = 2.7 m. MA A Answer: (a) VA = (b) Vmid i LAB i Wo B LBC mm. mm.

By using three moment equation, determine the deflection three meters to the left of roller support

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The motor compartment rail must meet the package constraints imposed by the suspension and powertrain. These constraints often force nonsymmetrical loading and section shape. For the illustrations shown in a and b determine the deflection at the tip of the beam and maximum direct stress and location for a 2000-N load. 40 x 80 x 1.5 mm 1 m Engine (a) Load application at centroid 2 |15° Section rotated 15°. Load application point through centroid of section (b) Engine

2 - Use double integration to determine the elastic curve of the cantilever beam under lateral loading, where w is the load intensity (per unit length) at the left end. Flexural rigidity is El. Show that the tip displacement is: y w w14 U(L)=-30EI

Determine the deflection at midspan for the beam of Problem 4–69 using Castigliano's theorem. Material of the beam is steel with E=30 Mpsi. w 180 lbf/in 1.375-in dia. r1.375-in dia. Problem 4-69 11.75-in dia. +3 in + 10 in 3 in

5. For the beam shown in the figure, determine the slope at A and B and the value of the maximum deflection. 150 lb 240 lb 0.3 k/ft -10 ft -8 ft- - 10 ft- E = 29,000 ksi | = 20 in

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