Engineering Mathematics

symmetrical load

Problem 868 | Deflection by Three-Moment Equation

Problem 868
Determine the values of EIδ at midspan and at the ends of the beam loaded as shown in Figure P-868.
 

868-simple-overhanging-beam-triangular-load.gif

 

Problem 855 | Continuous Beams with Fixed Ends

Problem 855
If the distributed load in Prob. 854 is replaced by a concentrated load P at midspan, determine the moments over the supports.
 

855-i-span.gif

 

Answers:
$M_1 = \dfrac{PL}{8} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{PL}{8} \cdot \dfrac{2}{\alpha + 2} = M_3$
 

Problem 854 | Continuous Beams with Fixed Ends

Problem 854
Solve for the moment over the supports in the beam loaded as shown in Fig. P-854.
 

854-i-span.gif

 

Answers:
$M_1 = \dfrac{w_o L^2}{12} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{w_o L^2}{12} \cdot \dfrac{2}{\alpha + 2} = M_3$
 

Problem 853 | Continuous Beams with Fixed Ends

Problem 853
For the continuous beam shown in Fig. P-853, determine the moment over the supports. Also draw the shear diagram and compute the maximum positive bending moment. (Hint: Take advantage of symmetry.)
 

853-shear-diagram.gif

 

Problem 836 | Reactions of Continuous Beams

Problem 836
For the continuous beam loaded as shown in Fig. P-816, determine the length x of the overhang that will cause equal reactions.
 

816-equal-moments-over-supports.gif

 

Problem 410 Pratt Roof Truss - Method of Joints

Problem 410
Determine the force in each member of the Pratt roof truss shown in Fig. P-410.
 

410-pratt-roof-truss.gif

 

Problem 715 | Distributed loads placed symmetrically over fully restrained beam

Problem 12
Determine the moment and maximum EIδ for the restrained beam shown in Fig. RB-012. (Hint: Let the redundants be the shear and moment at the midspan. Also note that the midspan shear is zero.)
 

715-restrained-beam-symmetrical-uniform-loads.gif

 

Problem 713 | Fully restrained beam with symmetrically placed concentrated loads

Problem 713
Determine the end moment and midspan value of EIδ for the restrained beam shown in Fig. PB-010. (Hint: Because of symmetry, the end shears are equal and the slope is zero at midspan. Let the redundant be the moment at midspan.)
 

713-fully-restrained-beams-symmetrical-point-loads.gif

 

Problem 542 | Friction on Wedges

Problem 542
What force P must be applied to the wedges shown in Fig. P-542 to start them under the block? The angle of friction for all contact surfaces is 10°.
 

542-wedge-syymetrically-placed.gif

 

Solution to Problem 691 | Beam Deflection by Method of Superposition

Problem 691
Determine the midspan deflection for the beam shown in Fig. P-691. (Hint: Apply Case No. 7 and integrate.)
 

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