Uniform Load

Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection

Situation
A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

Given Beam Properties:
Area = 8,530 mm2
Depth = 306 mm
Flange Width = 204 mm
Flange Thickness = 14.6 mm
Moment of Inertia, Ix = 145 × 106 mm4
Modulus of Elasticity, E = 200 GPa

1.   What is the maximum flexural stress (MPa) in the beam?

A.   107 C.   142
B.   54 D.   71

2.   To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

Given Column Properties:
Outside Diameter = 200 mm
Thickness = 10 mm
Height = 4 m
A.   4.7 C.   18.8
B.   9.4 D.   2.8

3.   How much is the maximum bending stress (MPa) in the propped beam?

A.   26.7 C.   15.0
B.   17.8 D.   35.6

 

Reactions of Tripod Made from Wood Planks

Situation
In the figure shown, each plank carries a uniform load of 100 N/m throughout its length. The supports are on the same plane.
 

eq-parallel-forces-tripod.gif
  1. Find the reaction at A.
    A. 900 N
    B. 800 N
    C. 1400 N
    D. 2400 N
     
  2. Find the reaction at B.
    A. 900 N
    B. 800 N
    C. 1400 N
    D. 2400 N
     
  3. Find the reaction at C.
    A. 900 N
    B. 800 N
    C. 1400 N
    D. 2400 N
     

Problem 860 | Deflection by Three-Moment Equation

Problem 860
Determine the value of EIδ at the end of the overhang and midway between the supports for the beam shown in Fig. P-860.
 

860-overhang-beam-given.gif

 

Problem 833 | Reactions of Continuous Beams

Problem 833
Refer to Problem 825 for which M2 = -980 lb·ft and M3 = -1082 lb·ft.
 

833-shear-diagram.gif

Problem 823 | Continuous Beam by Three-Moment Equation

Problem 823
A continuous beam simply supported over three 10-ft spans carries a concentrated load of 400 lb at the center of the first span, a concentrated load of 640 lb at the center of the third span and a uniformly distributed load of 80 lb/ft over the middle span. Solve for the moment over the supports and check your answers using the results obtained for Problems 819 and 822.
 

823-continuous-beam.gif

 

Problem 822 | Continuous Beam by Three-Moment Equation

Problem 822
Solve Prob. 821 if the concentrated load is replaced by a uniformly distributed load of intensity wo over the middle span.
 

822-beta-alpha-span-uniform-load.gif

 

Answers:
$M_2 = -\dfrac{w_o L^2}{4} \cdot \dfrac{1 + 2\beta}{4(\alpha + 1)(1 + \beta) - 1}$

$M_3 = -\dfrac{w_o L^2}{4} \cdot \dfrac{1 + 2\alpha}{4(1 + \alpha)(1 + \beta) - 1}$
 

Problem 820 | Continuous Beam by Three-Moment Equation

Problem 820
Solve Prob. 819 if the concentrated load is replaced by a uniformly distributed load of intensity wo over the first span.
 

820-continuous-beam-uniform-load.gif

 

Problem 816 | Continuous Beam by Three-Moment Equation

Problem 816
Determine the lengths of the overhangs in Fig. P-816 so that the moments over the supports will be equal
 

816-equal-moments-over-supports.gif

 

Problem 1007 | Flexural stresses developed in the wood and steel fibers

Problem 1007
A uniformly distributed load of 300 lb/ft (including the weight of the beam) is simply supported on a 20-ft span. The cross section of the beam is described in Problem 1005. If n = 20, determine the maximum stresses produced in the wood and the steel.
 

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