Uniformly Varying Load

Solution to Problem 630 | Moment Diagrams by Parts

Problem 630
For the beam loaded as shown in Fig. P-630, compute the value of (AreaAB)barred(X)A . From the result determine whether the tangent drawn to the elastic curve at B slopes up or down to the right. (Hint: Refer to the deviation equations and rules of sign.)
 

Overhang beam with point load at free end

 

Solution to Problem 629 | Moment Diagrams by Parts

Problem 629
Solve Prob. 628 if the sense of the couple is counterclockwise instead of clockwise as shown in Fig. P-628.
 

Simple beam loaded with triangular and moment loads

 

Solution to Problem 628 | Moment Diagrams by Parts

Problem 628
For the beam loaded with uniformly varying load and a couple as shown in Fig. P-628 compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
 

Simple beam loaded with triangular and moment loads

 

Solution to Problem 627 | Moment Diagram by Parts

Problem 627
For the beam loaded as shown in Fig. P-627compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Resolve the trapezoidal loading into a uniformly distributed load and a uniformly varying load.)
 

627-uniformly-varying.gif

 

Moment Diagram by Parts

The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

Solution to Problem 620 | Double Integration Method

Problem 620
Find the midspan deflection δ for the beam shown in Fig. P-620, carrying two triangularly distributed loads. (Hint: For convenience, select the origin of the axes at the midspan position of the elastic curve.)
 

Beam loaded with symmetrical triangular load

 

Solution to Problem 503 | Flexure Formula

Problem 503
A cantilever beam, 50 mm wide by 150 mm high and 6 m long, carries a load that varies uniformly from zero at the free end to 1000 N/m at the wall. (a) Compute the magnitude and location of the maximum flexural stress. (b) Determine the type and magnitude of the stress in a fiber 20 mm from the top of the beam at a section 2 m from the free end.
 

Solution to Problem 445 | Relationship Between Load, Shear, and Moment

Problem 445
Beam carrying the loads shown in Fig. P-445.
 

 
445-simple-beam-uniform-and-trapezoidal-loads.gif

 

Solution to Problem 444 | Relationship Between Load, Shear, and Moment

Problem 444
Beam loaded as shown in Fig. P-444.

 

Solution to Problem 443 | Relationship Between Load, Shear, and Moment

Problem 443
Beam carrying the triangular loads shown in Fig. P-443.

 

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