simple beam

Simply Supported Beam with Support Added at Midspan to Prevent Excessive Deflection

Situation
A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.
1.   To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

A.   64.5 C.   258.0
B.   96.8 D.   86.0

2.   Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

A.   96.75 C.   108.84
B.   54.42 D.   77.40

3.   Calculate the reaction (kN) at the added support.

A.   48.38 C.   161.2
B.   96.75 D.   80.62

 

Example 01: Spacing of Screws in Box Beam made from Rectangular Wood

Problem
A concentrated load P is carried at midspan by a simply supported 4-m span beam. The beam is made of 40-mm by 150-mm timber screwed together, as shown. The maximum flexural stress developed is 8.3 MPa and each screw can resist 890 N of shear force.
 

spacing-of-bolts-001-box-beam-cross-section.gif

 

  1.   Determine the spacing of screws at A.
  2.   Determine the spacing of screws at B.

 

Example 02: Required Diameter of Circular Log Used for Footbridge Based on Shear Alone

Problem
A wooden log is to be used as a footbridge to span 3-m gap. The log is required to support a concentrated load of 30 kN at midspan. If the allowable stress in shear is 0.7 MPa, what is the diameter of the log that would be needed. Assume the log is very nearly circular and the bending stresses are adequately met. Neglect the weight of the log.
 

beam-001-circular-log-shear-stress.gif

 

Influence Lines for Beams

A downward concentrated load of magnitude 1 unit moves across the simply supported beam AB from A to B. We wish to determine the following functions:

  • reaction at A
  • reaction at B
  • shear at C and
  • moment at C

when the unit load is at a distance x from support A. Since the value of the above functions will vary according to the location of the unit load, the best way to represent these functions is by influence diagram.
 

il-beam-moment-at-c.gif

 

Problem 906 | Combined Axial and Bending

Problem 906
For the 2-in. by 6-in. wooden beam shown in Fig. P-906. Determine the normal stress at A and B. Are these the points of maximum normal stress? If not, where are they located and what are their values?
 

906-beam-with-inclined-load.gif

 

Problem 905 | Combined Axial and Bending

Problem 905
A wooden beam 100 mm by 200 mm, supported as shown in Figure P-905, carries a load P. What is the largest safe value of P is the maximum stress is not to exceed 10 MPa?
 

905-simple-beam-inclined-load.jpg

 

Problem 861 | Deflection by Three-Moment Equation

Problem 861
For the beam shown in Fig. P-861, determine the value of EIδ at 2 m and 4 m from the left support.
 

861-simple-beam-given.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.
 

Problem 1003 | Maximum stresses in wood and steel of composite beam

Problem 1003
A simply supported beam 4 m long has the cross section shown in Fig. P-1002. It carries a uniformly distributed load of 20 kN/m over the middle half of the span. If n = 15, compute the maximum stresses in the wood and the steel.
 

Problem 711 | Cantilever beam with free end on top of a simple beam

Problem 711
A cantilever beam BD rests on a simple beam AC as shown in Fig. P-711. Both beams are of the same material and are 3 in wide by 8 in deep. If they jointly carry a load P = 1400 lb, compute the maximum flexural stress developed in the beams.
 

The ends of cantilever beam rests on top of simple beam at the third point.

 

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