**Problem 1:**A 10 ft. long simply supported laminated wooden beam consists of eight 1.5 in. by 6 in. planks glued together to form a section 6 in. by 12 in. deep, as shown. The beam carries a 9 kip concentrated load at midspan. At section \( a-a \), located 2.5 ft. from pin support \( A \), determine:a) The horizontal shear stress in the glue joints at \( b, c, \) and \( d \).b) The maximum horizontal shear stress in the cross section.**Diagram Explanation:**The diagram consists of a side view and a cross-sectional view of a simply supported beam. - **Side View:** - The beam is 10 ft. long, simply supported at both ends (labeled \( A \) and \( C \)). - Support \( A \) is a pin support, and support \( C \) is a roller. - A 9 kip concentrated load is applied at the midpoint of the beam. - Section \( a-a \) is marked 2.5 ft. from support \( A \) and 5 ft. from the midpoint load.- **Cross-Sectional View:** - The cross section of the beam is rectangular, measuring 6 in. wide and 12 in. deep. - The cross section is composed of eight planks, each 1.5 in. thick. - The planks are glued together horizontally, and glue joints are labeled at points \( b, c, \) and \( d \). - The diagram shows typical plank thickness (1.5 in.) and marks critical measurement points.This educational problem focuses on evaluating the horizontal shear stress at specified glue joints and determining the maximum horizontal shear stress across the beam's section under a given load.

Given data: b=6 inh=12 in10 ft wooden beam beam carries 9 kip concentrated load at midspan∑ Fv=0RA+RC=9∑ MA=09*5=RC*10RC=9*510RC=4.5 Kipsubstitue in RA+RC=9RA+4.5=9RA=9-4.5RA=4.5 kipshear fore at point P=RA=4.5 kipa)The horizontal shear stress in the glue joints at b,c and dshear stress at b:τ=sf AyI*bIxx=bh312 =6*12312 =864 in4Ay=(6-4.5)*6*4.5+6-4.52 =47.25 in3τb=sf AyI*b =4.5*47.25864*6τb=0.0411 ksi shear stress at c:τc=sf AyI*bA=6*(6-1.5)A=27 in2y=1.5+6-1.52 =3.75 inτc=sf AyI*b =4.5*27*3.75864*6τc=0.0878 ksi shear stress at d:τd=sf AyI*bA=6*(6-3)A=18 in2y=3+6-32y=4.5 inτd=sf AyI*b =4.5*18*4.5864*6τd=0.0703 ksib)The maximum horizontal shear stress in the cross section:τmax=sf AyI*bA=6*6A=36 in2y=62=3 inτmax=sf AyI*b =4.5*36*3864*6τmax=0.0937 ksi

Engineering

Mechanical Engineering

Problem 1: A 10 ft. long simply supported laminated wooden beam consists of eight 1.5in. by 6 in. planks glued together to form a section 6 in. by 12 in. deep, as shown. The beam carries a 9 kip concentrated load at midspan. At section a-a, located 2.5 ft. from pin support A, determine: a) The horizontal shear stress in the glue joints at b, c, and d. b) The maximum horizontal shear stress in the cross section. 9 kips 2.5 ft a 5 ft B 5 ft 1.5 in. (typ) 12 in. Z 6 in. b с d

Problem 1: A 10 ft. long simply supported laminated wooden beam consists of eight 1.5in. by 6 in. planks glued together to form a section 6 in. by 12 in. deep, as shown. The beam carries a 9 kip concentrated load at midspan. At section a-a, located 2.5 ft. from pin support A, determine: a) The horizontal shear stress in the glue joints at b, c, and d. b) The maximum horizontal shear stress in the cross section. 9 kips 2.5 ft a 5 ft B 5 ft 1.5 in. (typ) 12 in. Z 6 in. b с d

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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**Problem 1:**

A 10 ft. long simply supported laminated wooden beam consists of eight 1.5 in. by 6 in. planks glued together to form a section 6 in. by 12 in. deep, as shown. The beam carries a 9 kip concentrated load at midspan. At section \( a-a \), located 2.5 ft. from pin support \( A \), determine:
a) The horizontal shear stress in the glue joints at \( b, c, \) and \( d \).
b) The maximum horizontal shear stress in the cross section.

**Diagram Explanation:**

The diagram consists of a side view and a cross-sectional view of a simply supported beam.

- **Side View:**
- The beam is 10 ft. long, simply supported at both ends (labeled \( A \) and \( C \)).
- Support \( A \) is a pin support, and support \( C \) is a roller.
- A 9 kip concentrated load is applied at the midpoint of the beam.
- Section \( a-a \) is marked 2.5 ft. from support \( A \) and 5 ft. from the midpoint load.

- **Cross-Sectional View:**
- The cross section of the beam is rectangular, measuring 6 in. wide and 12 in. deep.
- The cross section is composed of eight planks, each 1.5 in. thick.
- The planks are glued together horizontally, and glue joints are labeled at points \( b, c, \) and \( d \).
- The diagram shows typical plank thickness (1.5 in.) and marks critical measurement points.

This educational problem focuses on evaluating the horizontal shear stress at specified glue joints and determining the maximum horizontal shear stress across the beam's section under a given load.

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