Solution to Problem 609 | Double Integration Method

Problem 609
As shown in Fig. P-609, a simply supported beam carries two symmetrically placed concentrated loads. Compute the maximum deflection δ.
 

Symetrically Placed Concentrated Loads

 

Solution to Problem 608 | Double Integration Method

Problem 608
Find the equation of the elastic curve for the cantilever beam shown in Fig. P-608; it carries a load that varies from zero at the wall to wo at the free end. Take the origin at the wall.
 

Cantilever Beam Loaded with Triangular Load

 

Solution to Problem 607 | Double Integration Method

Problem 607
Determine the maximum value of EIy for the cantilever beam loaded as shown in Fig. P-607. Take the origin at the wall.
 

Cantilever Beam with Point Load

 

Solution to Problem 606 | Double Integration Method

Problem 606
Determine the maximum deflection δ in a simply supported beam of length L carrying a uniformly distributed load of intensity wo applied over its entire length.
 

Solution to Problem 605 | Double Integration Method

Problem 605
Determine the maximum deflection δ in a simply supported beam of length L carrying a concentrated load P at midspan.
 

Double Integration Method | Beam Deflections

The double integration method is a powerful tool in solving deflection and slope of a beam at any point because we will be able to get the equation of the elastic curve.
 

In calculus, the radius of curvature of a curve y = f(x) is given by
 

Beam Deflections

Deflection of Beams
The deformation of a beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.
 

Solution to Problem 599 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 599
A beam is formed by bolting together two W200 × 100 sections as shown in Fig. P-599. It is used to support a uniformly distributed load of 30 kN/m (including the weight of the beam) on a simply supported span of 10 m. Compute the maximum flexural stress and the pitch between bolts that have a shearing strength of 30 kN.
 

Wide Flange on top of the other and bolted together

 

Solution to Problem 598 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 598
As shown in Fig. P-598, two C380 × 60 channels are riveted together by pairs of 19-mm rivets spaced 200 mm apart along the length of the beam. What maximum vertical shear V can be applied to the section without exceeding the stresses given in Illustrative Problem 591?
 

Bolted Back-to-back Channels

 

Solution to Problem 597 | Spacing of Rivets or Bolts in Built-Up Beams

Problem 597
A plate and angle girder similar to that shown in Fig. 5-32 is fabricated by riveting the short legs of four 125 × 75 × 13 mm angles to a web plate 1000 mm by 10 mm to form a section 1020 mm deep. Cover plates, each 300 mm × 10 mm, are then riveted to the flange angles making the overall height 1040 mm. The moment of inertia of the entire section about the NA is I = 4770 × 106 mm4. Using the allowable stresses specified in Illustrative Problem 591, determine the rivet pitch for 22-mm rivets, attaching the angles to the web plate at a section where V = 450 kN.
 

Built-up Girder from Plate and Angles

 

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