1. For the following beam structure: a) Determine the internal normal force (N), shear force (V), and bending moment (M) at point C of the beam. b) Draw the shear-force (V-M) diagram from point C to point D (end of the beam). Include the beginning and end magnitudes for the V and M on the graphs, and include the mathematical function for each trend. (Note: the beam is loaded with two different distributed loads and two separate concentrated loads and a moment couple at the end of the beam). 2 kN/m immuta •B A 5 m 5 m 7.5 kN 1 kN/m 1 m -3 m 6 kN 40 kN-m

1. For the following beam structure: a) Determine the internal normal force (N), shear force (V), and bending moment (M) at point C of the beam. b) Draw the shear-force (V-M) diagram from point C to point D (end of the beam). Include the beginning and end magnitudes for the V and M on the graphs, and include the mathematical function for each trend. (Note: the beam is loaded with two different distributed loads and two separate concentrated loads and a moment couple at the end of the beam). 2 kN/m immuta •B A 5 m 5 m 7.5 kN 1 kN/m 1 m -3 m 6 kN 40 kN-m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

1. For the following beam structure:
a) Determine the internal normal force (N), shear force (V), and bending moment (M) at
point C of the beam.
b) Draw the shear-force (V-M) diagram from point C to point D (end of the beam).
Include the beginning and end magnitudes for the V and M on the graphs, and include
the mathematical function for each trend.
(Note: the beam is loaded with two different distributed loads and two separate concentrated loads
and a moment couple at the end of the beam).
7.5 kN
2 kN/m
1 kN/m
mmmlak.
•C
•B
A
5 m
5 m
1 m
-3 m
6 kN
40 kN-m

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SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR ANSWER FOR BETTER UNDERSTANDING.
Replace the loading by an equivalent resultant force and couple moment acting at point 0. Solution Strategy:1. Break the distributed load into “primal” geometric shapes. This problem lends itself to analysis in 3 primal shapes.2. The areas below the load profiles will tell you the magnitudes of the equivalent concentrated loads.3. The position of the individual concentrated loads resulting from breaking up the given load profile will be located at the centroid of each primal.4. Once you have the equivalent concentrated loads and positions for the three primals you can find the resultant force and moment about ? in one of two ways:a. Find a single equivalent force and position (like you did for 11-W) and then relocate this single force to ?? using the techniques from topic 10.b. Use the techniques from topic 10 directly on the three equivalent concentrated loads you found in steps 2 & 3.