The pin-connected structure shown below is loaded by a horizontal load of 10 kips and a vertical load of 5 kips at point 1. The X, Y coordinates in ft. are shown next to each node. EA 10,000 kips for each member. a) Using the direct stiffness method, determine the 2 x 2 global stiffness matrix [K]. Clearly indicate its units. b) By inverting the global stiffness matrix [K] obtained in a), determine the 2 x 2 global flexibility matrix [F]. Clearly indicate its units. c) Using the global flexibility matrix [F] obtained in b) calculate the horizontal and vertical deflections in inches at point 1. d) Using the element stiffness matrix of member 1, determine the horizontal and vertical support reactions at point 2. Clearly indicate their directions. e) Using the elements stiffness matrix for element 1, determine the axial force in member 1. Clearly indicate if it is in tension or compression. 5 kips 1 2 (0, 0) Ⓒ (0,-5) (3,4) 10 kips D² LD

The pin-connected structure shown below is loaded by a horizontal load of 10 kips and a vertical load of 5 kips at point 1. The X, Y coordinates in ft. are shown next to each node. EA 10,000 kips for each member. a) Using the direct stiffness method, determine the 2 x 2 global stiffness matrix [K]. Clearly indicate its units. b) By inverting the global stiffness matrix [K] obtained in a), determine the 2 x 2 global flexibility matrix [F]. Clearly indicate its units. c) Using the global flexibility matrix [F] obtained in b) calculate the horizontal and vertical deflections in inches at point 1. d) Using the element stiffness matrix of member 1, determine the horizontal and vertical support reactions at point 2. Clearly indicate their directions. e) Using the elements stiffness matrix for element 1, determine the axial force in member 1. Clearly indicate if it is in tension or compression. 5 kips 1 2 (0, 0) Ⓒ (0,-5) (3,4) 10 kips D² LD

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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Question

Problem No. 2
The pin-connected structure shown below is loaded by a horizontal load of 10 kips and a vertical
load of 5 kips at point 1. The X, Y coordinates in ft. are shown next to each node. EA = 10,000
kips for each member.
a) Using the direct stiffness method, determine the 2 x 2 global stiffness matrix [K]. Clearly
indicate its units.
b) By inverting the global stiffness matrix [K] obtained in a), determine the 2 x 2 global
flexibility matrix [F]. Clearly indicate its units.
c) Using the global flexibility matrix [F] obtained in b) calculate the horizontal and vertical
deflections in inches at point 1.
d) Using the element stiffness matrix of member 1, determine the horizontal and vertical support
reactions at point 2. Clearly indicate their directions.
e) Using the elements stiffness matrix for element 1, determine the axial force in member 1.
Clearly indicate if it is in tension or compression.
5 kips
2
(0, 0)
(0,-5)
(3, 4)
10 kips
D²
Lo
LODI

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Step 1: Determining the global stiffness matrix [K]:

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Step 2: Determining the global flexibility matrix [F]

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Step 3: Calculating the deflections at point 1

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Step 4: Calculating the support reactions at point 2:

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Step 5: Determining the axial force in member 1

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