4 Resultant of Parallel Force System PDF

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#4 Compute resultant of parallel force system.

CESTAT30 – STATICS OF RIGID BODIES FLEX Course Material

Locate and draw the resultant parallel force system.

RESULTANT OF PARALLEL FORCE SYSTEM

Marvin M. Bartido, RCE

1ST TERM AY 2020-2021

PRE-ASSESSMENT

Pr Pre-a e-a e-asses sses ssessm sm smen en entt No. 4 Parallel Force System

Which of the following is/are a parallel force system? a.

b.

c.

d.

Table of Contents Resultant of Parallel Force System Types of Loads Sample Problems

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“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

RESULTANT OF PARALLEL FORCE SYSTEM

Parallel forces – one in which the action lines of all the forces are parallel. 𝑅𝑥 = Σ 𝐹𝑥 𝑅𝑦 = Σ 𝐹𝑦 𝑅=

𝑅𝑥 2 + 𝑅𝑦 2

Use Varignon’s Theorem to determine the location/position of the resultant 𝑅𝑑 = σ 𝐹𝑑 For resultant of parallel force system: • 𝑅 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 • 𝐷𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 (↑↓→←) • 𝑑 (𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑜𝑟 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛) For summation, use the sign convention: 𝑭𝒙 →

+

←

-

𝑭𝒚

↑

+

↓

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“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

SAMPLE PROBLEM No. 1 Determine the resultant of the parallel forces system acting on the bar AB shown below.

Find: Resultant Solution: 𝑅𝑦 = σ 𝐹𝑣 ↑ +

𝑀𝐴 = 𝑅𝑑 = σ 𝐹𝑑 ↻ + 60𝑑 = 10 2 − 10 5 + 40(8) 𝑑 = 4.8333 𝑚 𝑓𝑟𝑜𝑚 𝑝𝑡. 𝐴

𝑅𝑦 = −20 − 10 + 10 − 40 𝑅𝑦 = −60 𝑁 𝑅𝑥 = 0

𝑅=

𝑅𝑥 2 + 𝑅𝑦 2

R

𝑅 = 𝑅𝑦 = −60𝑁 𝑅 = 60𝑁 ↓

d 5

“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

SAMPLE PROBLEM No. 2 A parallel force system acts on the lever shown below. Determine the magnitude and position of the resultant.

Find: Resultant Solution:

𝑅𝑦 = σ 𝐹𝑣 ↑ +

𝑀𝐴 = 𝑅𝑑 = σ 𝐹𝑑 ↻ + 110𝑑 = 30 2 + 60 5 − 20 7 + 40(11) 𝑑 = 6 𝑚 𝑓𝑟𝑜𝑚 𝑝𝑡. 𝐴

𝑅𝑦 = −30 − 60 + 20 − 40 𝑅𝑦 = −110 𝑁 𝑅𝑥 = 0 𝑅=

𝑅𝑥 2 + 𝑅𝑦 2

R

𝑅 = 𝑅𝑦 = −110𝑁 𝑅 = 110𝑁 ↓

d 6

“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

Types of Loads

Note: Uniformly distributed load, triangular distributed load and trapezoidally distributed load can be converted into its equivalent point load.

𝑅 = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 1 = 𝑤𝑜 ∙ 𝐿 2 2𝐿 𝑑 = 3 (location of the point load from the left)

𝑅 = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 = 𝑤𝑜 ∙ 𝐿 𝐿 𝑑 = (location of the point 2 load from the left)

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“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

SAMPLE PROBLEM No. 3 A beam of length L supports a load which varies from w N/m at the right end to zero at the left end. Determine the magnitude and position of the resultant load.

Find: Resultant Solution: 𝑅= 𝑑=

1 𝑤𝐿 2 2 𝐿 from 3

(Newton) pt. O

(meter)

R d

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“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

SAMPLE PROBLEM No. 4 The beam AB supports a load which varies from an intensity of 50N/m to 200N/m. Calculate the magnitude and position of the resultant load.

Find: Resultant Solution 1

Solution 2

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“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

R

Solution 1 d

𝑹𝟏

R

𝑹𝟐

d

𝑹𝟏

𝒅𝟏 𝒅𝟏

𝒅𝟐

𝒅𝟐

𝑅1 = 50 1

𝑁 𝑚

12 𝑚 = 600𝑁

𝑅2 = (150 2

𝑁 ) 𝑚

𝑀𝐴 = 𝑅𝑑 = σ 𝐹𝑑 ↻ +

12 𝑚 = 900𝑁

1500𝑑 = 600 2

12 2

+

𝑅𝑦 = σ 𝐹𝑣 ↑ +

900

𝑅𝑦 = −600 − 900 𝑅𝑦 = −1500𝑁 𝑅 = −1500 𝑁 𝑜𝑟 1500𝑁 ↓

𝑑 = 7.2 𝑚 𝑓𝑟𝑜𝑚 𝑝𝑡. 𝐴

10

3

(12)

𝑹𝟐

“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.” Jeremiah 29:11

Solution 2 Try solving this on your own. The answer is the same as in Solution 1

R 𝑹𝟐

d

𝑹𝟏 𝒅𝟏

𝒅𝟐

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ASSESSMENT TASK

Assess Assessmen men mentt Task No. 4 Topic Learning Outcome: Compute the resultant of parallel force system 1. Determine the resultant of the parallel forces system acting on the bar AB shown below and the position of the resultant from point A.

2. A parallel force system acts on the lever shown below. Determine the magnitude and position of the resultant from point B.

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ASSESSMENT TASK

3. A beam of length L = 20 ft supports a load which varies from w = 125 N/m at the left end to zero at the right end. Determine the magnitude and position of the resultant load.

4. The beam AB supports a load which varies from an intensity of 333 lb/ft to 88 lb/ft. Calculate the magnitude and position of the resultant load.

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