file lock을 쓰레드에서는 쓸수 없나요?

다음과 같은 소스에서

#include
#include
#include
#include
#include

void *do_write(void *data)
{
int fp;
struct flock lType;

fp = open("./test.txt", O_RDWR | O_CREAT);

lType.l_type = F_WRLCK;
lType.l_whence = SEEK_SET;
lType.l_start = 2;
lType.l_len = 2;

fcntl(fp, F_SETLKW, lType);
printf("1 is lock now!!\n");
sleep(4);

lType.l_type = F_UNLCK;
fcntl(fp, F_SETLKW, lType);
printf("1 is unlock now!!\n");
sleep(5);

}

void *do_read(void *data)
{
int fp;
struct flock lType;

fp = open("./test.txt", O_RDWR | O_CREAT);

sleep(2);

lType.l_type = F_WRLCK;
lType.l_whence = SEEK_SET;
lType.l_start = 2;
lType.l_len = 2;

printf("2 is try lock now!!\n");
fcntl(fp, F_SETLKW, lType);
printf("2 is get lock now!!\n");
sleep(2);

lType.l_type = F_UNLCK;
fcntl(fp, F_SETLKW, lType);
printf("2 is unlock now!!\n");
sleep(5);

}

int main()
{
pthread_t p_thread[5];
int thr_id;
int status;
int a = 1;
int b = 2;
FILE *fp;

char arr[10];

fp = fopen("./test.txt", "w");
fprintf(fp, "123456789");
fclose(fp);

thr_id = pthread_create(&p_thread[0], NULL, do_write, (void *)&a);
thr_id = pthread_create(&p_thread[1], NULL, do_read, (void *)&b);

pthread_join(p_thread[0], (void **) status);
pthread_join(p_thread[1], (void **) status);

return 0;
}

컴파일후 실행을 하니
$ ./a.out
1 is lock now!!
2 is try lock now!!
2 is get lock now!!
1 is unlock now!!
2 is unlock now!!
$

위와 같은 결과가 나옵니다..

저의 생각으로는
1 is lock now!!
2 is try lock now!!
1 is unlock now!!
2 is get lock now!!
2 is unlock now!!

이렇게 나와야 할것 같거든요....

뭐가 잘못된건지.. 아니면 쓰레드에서는 file lock을 쓸수 없는건가요?