1/30/23, 10:17 AM
120 kN/m B D 22 m- -2.4 m– -2 m→...
Question
Determine the reactions in each support.
solution
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Step 1
On a shear force diagram, a point load or reaction causes an abrupt change in the
graph in the direction of the applied load. A uniformly distributed load acting on a
beam is represented by a straight line shear force with a negative or positive slope
that is equal to the load per unit length. One of the most basic structures is the simply
supported beam. It only has two supports, one at each end. The first is a pinned
support, and the second is roller support. This configuration prevents the beam from
moving vertically at both ends while allowing it to rotate freely. If a support prevents
a body from translating in a given direction, a force is developed on the body in that
direction.
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Step 2
A support response can be defined as a force acting on a support or a consequent
restraining end moment caused by a restricted ability to move. Support responses in
structural systems are in balance with the external forces acting on the structure. One
of the most basic constructions is the simply supported beam. It only has two
supports, one at each end. The first is a pinned support, and the second is roller
support. This arrangement prevents the beam from moving vertically at both ends
while allowing it to spin freely.
Calculate the support reaction
∑𝐹 𝑥 = 0𝑅𝐴 + 𝑅𝐵 = 120 × 2 . 4𝑅𝐴 + 𝑅𝐵 = 288 𝐾𝑁 ∑𝑀𝐴 = 02 . 4 × 120 × 2 . 2 +
2.4
2
= 𝑅𝐷 × 6 . 8𝑅𝐷 =
60 . 14 𝐾𝑁𝑅𝐴 =
144 𝐾𝑁
Calculate shear force
Shear force is a force that acts in a direction parallel to (over the top of) a surface or
cross-section of a body, such as an airflow pressure over an airplane wing. The term
shear refers to the notion that such a force can cut or shear through the surface or
item under strain. The shear force at each point on a beam is calculated as the total of
all transverse forces operating on either side of the section. The shear force sign
convention is shown below. The bending moment diagram is a graphical depiction of
the bending moment operating on the beam.
𝑃𝑜𝑖𝑛𝑡 𝐴, 𝑆𝐹𝐴 =
144 𝐾𝑁𝑃𝑜𝑖𝑛𝑡 𝐵, 𝑆𝐹𝐵 =
144 𝐾𝑁𝑃𝑜𝑖𝑛𝑡 𝑥 𝑖𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐵 𝑎𝑛𝑑 𝐶, 𝑆𝐹𝑥 =
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144 - 120𝑥𝐴𝑡 𝑥 = 1 . 2, 𝑆𝐹 = 0𝐴𝑡 𝑥 = 2 . 4, 𝑆𝐹 =
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120 kN/m B D 22 m- -2.4 m– -2 m→...
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Step 3
Bending Moment Diagram (BMD): A Bending Moment Diagram (BMD) is a
diagram that shows the variation of bending moment along the length of a beam
(BMD). A moment is equal to a force multiplied by the length of the line
perpendicular to the force that passes through the point of reaction. The internal
reaction to a bending load is referred to as a bending moment. As a result, it is acting
on a surface that is normal to the part's neutral axis. When an axial load is applied to
a beam, the bending stress results in two types of bending moments: sagging and
hogging. Sagging is defined as a positive bending moment, whereas hogging is
defined as a negative bending moment.
Calculate Bending moment
𝑃𝑜𝑖𝑛𝑡 𝐴, 𝐵𝑀𝐴 = 0𝑃𝑜𝑖𝑛𝑡 𝐵, 𝐵𝑀𝐵 =
𝑅𝐴 × 2 . 2 = 316 . 8 𝐾𝑁 . 𝑚𝐴𝑡 𝑝𝑜𝑖𝑛𝑡 𝑥 𝑖𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐵 𝑎𝑛𝑑 𝐶𝑀𝑥 = 144 × 2 . 2 + 𝑥 - 120 ×
𝑥2
2
𝐴𝑡 𝑥 = 1 . 2𝑚, 𝑀 =
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Step 4
Shear and bending moment diagrams are analytical tools that are used in conjunction
with structural analysis to assist in a structural design by determining the value of
shear force and bending moment at a given point of a structural element such as a
beam. Shear Force Diagram (SFD): A Shear Force Diagram depicts the variation of
shear force along the length of a beam (SFD). Bending Moment Diagram (BMD): A
Bending Moment Diagram (BMD) is a diagram that shows the variation of bending
moment along the length of a beam (BMD).
Shear force and bending moment diagram
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120 kN/m B D 22 m- -2.4 m– -2 m→...
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